Logarithms Questions and Answers
Math
LogarithmsGiven e^2x-5 3y, which of the following represents the exponential equation rewritten into logarithmic form?
In (3y)=2x-5
log(2x - 5) = e
In(3e)=2x-5
In (y³) = 2x - 5
Math
LogarithmsGiven each logarithm equation below, match
the logarithm with its base.
Equation A) 5 log, 2 = x
Equation B) log₂ (3) = 5x
Equation C) In (3x) = 2
Equation D) log(5x) = 3
Equation E) x log5 (2) = 3
Math
LogarithmsSolve for x.
log5 (x+3)=1-log5 (x+7)
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Math
LogarithmsEvaluate the expression, reduce to simplest form.
Do these WITHOUT your calculator. It is about understanding the concepts, not being able to push buttons.
(a) 2¹og₂ 3
Your answer is
(b) 10log 7
Your answer is
(C) eln 4
Your answer is
Math
LogarithmsUse the change-of-base formula to convert to natural logarithms. Then use a calculator to find the value of log9, (73).
Math
LogarithmsSolve the exponential equation by taking the logarithm of both sides.
You will need to use a scientific calculator for this problem.
e0.07 = 13
Your answer must be correct to at least 3 decimal places.
Recall the change of base formula for logarithms: logb (A) can be calculated as In(A)/In (b)
Math
LogarithmsIn 2012, the population of a city was 5.92 million. The exponential growth rate was 3.24% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9 million?
d) Find the doubling time.
a) The exponential growth function is P(t) = 5.92 e 0.0324t, where t is in terms of the number of years since 2012 and P(t) is the population in millions.
(Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)
b) The population of the city in 2018 is 7.2 million.
(Round to one decimal place as needed.)
c) The population of the city will be 9 million in about years after 2012
(Round to one decimal place as needed.)
Math
LogarithmsEvaluate each logarithm using properties of logarithms and the following facts.
loga (x) = 3.1 loga (y) = 1.2
loga(z) = 2.1
(a) loga (yz)
(b) loga ((z/y)
(c) loga (y)8
(d) loga (3√z)
Math
LogarithmsUse the change of base formula to compute log(3)1/8
Round your answer to the nearest thousandth.
Math
Logarithmsfind the domain of each logarithmic function.
f(x) = log5 (x+4)
f(x) = log5 (x+6)
f(x) = log (2 - x)
f(x) = log (7 − x)
f(x) = ln(x - 2)²
f(x) = ln(x – 7)²
Math
LogarithmsIn Exercises 10-8, write each equation in its equivalent
exponential form.
1. 4 = log₂16
2.6 = log₂64
3. 2 = log3x
4. 2 = logga
5.5 = log 32
6. 3 = log 27
7. log6216 = y
8. log5125 = y
Math
LogarithmsSolve the following logarithmic equation.
log x+ log (x-48)=2
Write the equation obtained after applying the definition of and the properties of logarithms.
(Simplify your answer. Do not factor.)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution. The solution set is the empty set, Ø.
Math
LogarithmsWrite the following expression as a single, simplified, logarithm.
log7 (3x¹y³) log7 (5x6y³)
Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.
Provide your answer below:
Math
LogarithmsQUESTION 8
1 POINT
- 3 days
Use the change of base formula to express log, 4 using In, the natural logarithm.
Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta
keyboard.
Provide your answer below:
0/34
Math
LogarithmsUse the properties of logarithms to completely expand log 3 11y7/p
Do not include any parentheses in your answer.
Note: If you are using log you need to type it in and use the subscript button on the keyboard.
Provide your answer below:
Math
LogarithmsUsing the definition of the logarithm, what expression should go in the blank below?
54 = 625
4 =
Provide your answer below:
Math
LogarithmsUse the change of base formula to express log6 8 using log, the common logarithm. Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.
Math
LogarithmsQuestion
Which of the following equations uses the inverse property of logarithms correctly?
Select all correct answers.
Select all that apply:
☐ 5¹0g, (9)
☐ 5log5 (9) — 9
glog5 (5) = 5
5log, (5) 9
log5 (95) = 9
log5 (5⁹) = 9
=
=
9
Math
LogarithmsSolve 9e7x = 17.
Round your answer to the nearest tenth. Do not include "=" in your answer. If necessary, include a leading 0 with any decimals less than 1. For example, 0.5 instead of.5.
Math
LogarithmsWrite log, A as a natural logarithm.
Note: When entering natural log in your answer, enter lowercase LN as "in". There is no "natural log" button on the Alta keyboard.
Math
LogarithmsEnter the single simplified logarithm expression which is equivalent to 3 In 10-4 In 2 - In 5.
Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta
keyboard.
Provide your answer below:
Math
LogarithmsSolve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to at least 4 decimal places.
6e^3n-2+3=15
Math
LogarithmsGraph f(x) = log5 (x) + 4 using transformations by first graphing the basic logarithmic
function (parent function), then the progression of transformations (in the correct order).
State the domain, range, and vertical asymptote and end behavior.
Math
LogarithmsExpress the following equations in logarithmic form:
(a) 4¹ = 256 is equivalent to the logarithmic equation:
(b) 10-2 = 0.01 is equivalent to the logarithmic equation:
Math
LogarithmsRewrite each of the following equations: (Make sure to preview each answer)
(a) Rewrite 4³ = 64 as a logarithmic equation:
(b) Rewrite log 0.0001 = - 4 as an exponential equation:
Math
LogarithmsThe wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, in
miles, that the tornado travels and S is the wind speed, in miles per hour.
If a tornado traveled 15 miles, what was its wind speed, in miles per hour? Round your answer to the nearest tenth.
Provide your answer below:
miles per hour
Math
LogarithmsEvaluate the expression without using a calculator.
log 31
log 31 =
(Type an integer or a simplified fraction.)
Math
LogarithmsSimplify. Enter the result as a single logarithm with a coefficient of 1.
To enter the log, click in the answer cell, then click on the small yellow arrow on the right
Then click the Functions tab to access the log. If needed, you can change the base.
Math
LogarithmsIs x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (You
don't need to solve this equation, just determine if x = 0 is a valid solution)
It can't be determined from the information given.
Yes, since log(2) and log(5) both exist as valid values for the logarithm.
No, because the logarithm of a negative value is undefined.
No, because log(0) is undefined.
Math
LogarithmsDoes the function f(x) = (0.68)* represent exponential growth, decay, or neither?
Impossible to determine with the information given
Exponential growth
Neither
Exponential decay
Math
LogarithmsStudents in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model
f(t) = 95-11 log10 (t + 1), 0 ≤t≤ 24
where t is the time in months.
Enter your answer as a decimal, rounded to one decimal place. Do part a without a calculator, but use a calculator for parts b and c.
(a) What is the average score on the original exam?
(b) What was the average score after 6 months?
(c) What was the average score after 18 months?
Math
LogarithmsUse the Product Rule of Logarithms to write the completely expanded expression equivalent to log5 (3x + 6y). Make sure to use parenthesis around your logarithm functions log(x + y).
Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.
Provide your answer below:
Math
LogarithmsRewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places.
y = 1.5(1.8)^x
y = (In 1.5)e^x In 1.8, y = 0.405e0.588x
y = 1.5e^x In 1.8, y = 1.5e^0.588x
y = 1.8e^x In 1.5 y = 1.8e^0.405x
y = 1.5e^1.8x, y = 1.52.718^0.588x
Math
LogarithmsAn exponential decay function can be used to model the number of grams of a
radioactive material that remain after a period of time. A radioactive isotope decays
over time, with the amount remaining after t years given by y = 100e -0.00012434t if
100 grams is the original amount. How much remains after 2000 years?
(a) The amount of a radioactive isotope remaining after 2000 years is
approximately grams.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Math
LogarithmsSolve for :
log(x) + log(x + 5) = 3
You may enter the exact value or round to 4 decimal places.
Math
LogarithmsWrite the following sum as a single logarithm. Assume all variables are positive.
log3(c) + log3(c + 7) =
The answer format in lowercase characters is: log_base (number)
Spaces in the answer are optional.
Math
LogarithmsBacteria are growing exponentially in an environment of unlimited space and food. The
doubling time is 1 hour.
a. If there are initially a milligrams of bacteria, express the mass of the bacteria as a
function of time t.
f(t) = x(2)^t
b. Use your answer to part (a) to complete the following equation whose solution is the time
at which there are 3x milligrams of bacteria.
3x
=
c. Solve you
bacteria.
t=
equation from part (b) for the time t at which there are 3x milligrams of
hours
d. Your answer to part (c) should be between 1 and 2 hours. Check that it is. Do you
understand why it has to be?
Math
Logarithms(a) Let B=5750(1.045) give the balance of a bank account after t years. If the formula for B is written B=5750e, estimate the value of k correct to four decimal places.
(b) The balance of a bank account after t years is given by the formula B = 8750e002. If the formula for B is written B= 87508, find b exactly, and give the value of b correct to decimal places.
Math
LogarithmsSolve the exponential equation. Leave your answer in exact form.
7* = 53
The exact solution is x = 0.
(Type an exact answer in simplified form.)
Math
LogarithmsUse the laws of logarithms to find the exact value of the expression 2 In (8e) - In (64) without using a calculator.
(Give an exact answer. Use symbolic notation and fractions where needed. Simplify your answer completely.)
2 In (8e) In (64) =
Math
LogarithmsWrite in exponential form.
-3= log 9 (1/729)
The logarithmic equation - 3= log g
1
729
is the same as the exponential equation
Math
LogarithmsGive the starting value a, the growth/decay rater, and the continuous growth/decay
rate k. If there is exponential is decay your growth rates should be negative. For help
entering logarithms, see help (logarithms)
Q = 0.15. (e0.549)t has:
a =
r =
k =
help (numbers)
help (numbers)
help (numbers)
Math
LogarithmsSolve the logarithmic equation.
113
2
log b3 =
b= (Type an integer or a simplified fraction.)