Logarithms Questions and Answers

Given 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

Given 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

Solve 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".

Evaluate 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

Use the change-of-base formula to convert to natural logarithms. Then use a calculator to find the value of log9, (73).

Solve 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)

In 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.)

Evaluate 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)

Use the change of base formula to compute log(3)1/8 Round your answer to the nearest thousandth.

Use the change of base formula to compute log3 4.

find 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

In 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

Solve 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.

Write 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:

QUESTION 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

Use 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:

Write the following as a single logarithm. log3 (4x²y) + log3 (5x³y²)

Using the definition of the logarithm, what expression should go in the blank below? 54 = 625 4 = Provide your answer below:

Evaluate log5 1/25 Write your answer in simplest form. Provide your answer below:

Use 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.

Question 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

Solve 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.

Write 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.

Enter 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:

Rewrite e^x = 20 using natural logs

Solve 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

Graph 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.

Express 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:

Rewrite 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:

The 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

Evaluate the expression without using a calculator. log 31 log 31 = (Type an integer or a simplified fraction.)

Simplify. 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.

Write the equation in logarithmic form. r=s The equation in logarithmic form is

Is 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.

Does the function f(x) = (0.68)* represent exponential growth, decay, or neither? Impossible to determine with the information given Exponential growth Neither Exponential decay

Students 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?

Use 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:

Write the expression as a single logarithm. log4(x²-4) - 6 log 4(x+2)

Rewrite 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

An 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.)

Solve for : log(x) + log(x + 5) = 3 You may enter the exact value or round to 4 decimal places.

Write 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.

Evaluate using your calculator and round to 4 decimal places. log14(41)=

Bacteria 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?

(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.

Solve the exponential equation. Leave your answer in exact form. 7* = 53 The exact solution is x = 0. (Type an exact answer in simplified form.)

Use 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) =

Write in exponential form. -3= log 9 (1/729) The logarithmic equation - 3= log g 1 729 is the same as the exponential equation

Give 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)

Solve the logarithmic equation. 113 2 log b3 = b= (Type an integer or a simplified fraction.)