Logarithms Questions and Answers

The intensity levels / of two earthquakes measured on a seismograph can be compared by the formula log(I₁/I₂)= M₁ - M₂ where M is the magnitude given by the Richter Scale. In August 2009, an earthquake of magnitude 6.1 hit Honshu, Japan. In March 2011, that same region experienced yet another, more devastating earthquake, this time with a magnitude of 9.0. How many times greater was the intensity of the 2011 earthquake? Round to the nearest whole number.

Determine the domain of the function f(x) = log((x+7)/(x-3))

The difference of magnitudes of earthquakes, according to the Richter scale, is given by M₁ - M₂ = log(I₁ / I₂). If Earthquake 1 has magnitude 6.5 and Earthquake 2 has magnitude 5.0, determine how many times greater the intensity of Earthquake 1 is than that of Earthquake 2.

The binary entropy function describes the expected amount of information provided by each flip of a coin when the probability of the "heads" face showing is p. It is given by H(p) = -plog₂ (p) - (1 - p) log₂ (1 - p). Compute the value of H(0.1), and round your answer to four decimal places.

Write as an exponential equation. log 8x = 1 The logarithmic equation log gx = 1 written as an exponential equation is

Write the difference as a single logarithm. log4(35)-log4 (5)

Find the value of the logarithmic expression. log 1/8^8

Simplify the following into a single logarithm: 3 log(4) + 2 log(x) log (4³x²) log(4³/x²) log (3.4.x²) log (3.4.2x) log (3.4/2x)

Rewrite the following equation in logarithmic form. 0.25 = 2-² Rewrite the following equation in exponential form. log₈ (512) = 3

What is the effect in the time required to solve a problem when you double the size of the input from n to 2n, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n is each of these function? [Express your answer in the simplest form possible, either as a ratio or a difference. Your answer may be a function of n or a constant.] a) log log n b) log n c) 100n d) n log n e) n² f) n³ g) 2ⁿ

Consider the equation 0.3 . e³ˣ = 27. Solve the equation for x. Express the solution as a logarithm in base-e. x = __________ Approximate the value of x. Round your answer to the nearest thousandth. x ≈ _____

Evaluate the logarithm. Round your answer to the nearest thousandth. 2 log₃ (1/52) ≈ _______

If X has a uniform distribution U(0, 1), find the pdf of Y = e^x.

Atmospheric pressure P in pounds per square inch is represented by the formula P=14.7e^-0.21x, where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.131 pounds per square inch? (Hint: there are 5,280 feet in a mile) The mountain is Number ___ feet high.

0.6 0.4 0.3 p= 0.2 0.3 0.3 0.2 0.3 0.4 The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 60% chance it will be good tomorrow, a 20% chance it will be indifferent, and a 20% chance it will be P = bad. If the weather is indifferent today, there is a 40% chance it will be good tomorrow, and a 30% chance it will be indifferent. Finally, if the weather is bad today, there is a 30% chance it will be good tomorrow and a 30% chance it will be indifferent. The stochastic matrix for this situation is shown to the right. In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? _______________% (Round to the nearest integer as needed.)

Tim deposits $2100 into a savings account with an annual rate of 2.62% compounded annually for 10 years. He then withdraws this money and places it in another bank account at the rate of 3.58% compounded bi-weekly for 5 years. Once it is in this new account he also starts making regular deposits of $50 at the end of each month. a. What is the future value after all 15 years? b. How much interest was made in total?

2. Consider a five-node element in one dimension. The element length is 4, with node 1 at x₁ = 2, X₂=3, x3 = 4, x4 = 5, x5 = 6. 2-1) Construct the shape functions for the element. 2-2) The temperatures at the nodes are given by 3 Te = 1 0 -1 2 .find the temperature field at x-3.5 using shape functions constructed in (2-1).

Logarithmic equations. Solve for x log₄₉(x+4)+log₄(x-2)=1/2

Solve the equation. log₈2x + log₈(x + 4) = 2 x = -4 x = 4 x = 4 and x = -8 x = -8

Express as a single logarithm and simplify: 1/3(log₄25+ log₄5) a)(1/3) log₄30 b)1/9log₄(5) c) 1 d) log₄5

All of the following are examples of logarithmic scales, except: a) The Richter Scale b) The pH Scale c) The Radioactive Scale d) The Decibel Scale

Rewrite the equation log₈₀ 100 = z in exponential form. a) 100 = 80 ᶻ b) z =80¹⁰⁰ c) z⁸⁰= 100 d) 80 = 100ᶻ

To three decimal places, the slope of the tangent to the curve f(x) = log₁₀x, at x=1 is: a) 0.868 b) 0.251 c) 1.000 d) 0.434

Use the one-to-one property of logarithms to solve the equation. log5(2n² - 10n) = log5 (-24+n²)

Use the definition of a logarithm to solve the equation. -2 log7 x = 8

Graph each logarithmic function. Find the domain and range. 24. y = log5 (x - 1) 25. y = 4 log x+5

A quotient function. The two functions that you must divide are... Logarithmic Functions: y= 25 log9 (x+11) Exponential Function: y=60^x State the Domain, Range and vertical or horizontal Asymptotes. Justify your answer with reference to your equation and graph. Provide a sketch of your function.

Solve the logarithmic equation. log 9(x+5)= log914 Determine the equation to be solved after removing the logarithm. (Type an equation. Do not simplify.) 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. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Exercise 2.6. Determine the fractional Taylor expansions for the following cases: (a) f(x)= x³, a = 0, and n = 2.8, (b) f(x) = sinx, a = 0, and n = 1.2.

Condense the expression to the logarithm of a single quantity. 1/2[9 In(x + 7) + In(x) - In(x⁹ – 5)]

log (3 + x) - log (x-4)= log2 (3/2) {11} Ø {-11)

Solve the exponential equation. 4 ^x + 4 = 5^ 2x + 5

Evaluate the expression without using a calculator. log 3 27 9 3 1/3 1

Write in logarithmic form. 1/9=3^-2 The logarithmic form is. (Use integers or fractions for any numbers in the expression.)

Evaluate the expression without using a calculator. log 3 729 log 3 729 =

Find the solution of the exponential equation 5e^x-4=12 The exact solution (using natural logarithms) is: x = The approximate solution, rounded to 4 decimal places is: x =

Estimate the instantaneous rate of change of f(x) = logx at x=100 0.0043 2 0.000087 0.00043

Write the equation in equivalent logarithmic form. 6=36^1/2 What is the equivalent logarithmic form?

Use the exponential decay model, A = Ao e^kt, to solve the following. The half-life of a certain substance is 19 years. How long will it take for a sample of this substance to decay to 88% of its original amount? It will take approximately___for the sample of the substance to decay to 88% of its original amount.

Solve the equation: log2 (3x-7)-log₂ (x+3)=1

Solve log 4x + log 13 = 0. Round to the nearest thousandth if necessary. 3.25 0.019 0.311 52

Choose the single logarithmic expression that is equivalent to the one shown. log 8+ log 3 log 11 log 5 log 24 log 8/3

How is the graph of log x + 6 translated from the graph of log x? shifted left 6 units shifted up 6 units shifted down 6 units shifted right 6 units

What is the solution of the equation 2 + 3x = 7? Round your answer to the nearest ten-thousandth. 1.4650 0.4522 0.2218 0.6826

Expand the logarithm. log 5x/4y log 5 + log x - log 4 - log y log 5 + log x - log 4 + log y log5/4 + log x - log y log 5x - log 4y

3. Complete the following table by converting from exponential form to logarithmic form or from logarithmic form to exponential form. Exponential Form Logarithmic Form (1/3)^-4 log25 5 =1/2 2^m =n logb 4 =a

7. Solve the exponential equations. Round to 4 decimal places when necessary. a)81^2x=27^2x-5 b) 4000 = 200e^8x c) 5^x = 35

Which is the logarithmic form of 64 = 1296? log6 1296 = 4 log 1296 = 4.6 log 1296 = 4 log4 1296 = 6

Solve log 3x - log 13 = 2. Round to the nearest thousandth if necessary. 29 433.333 6.527 10.914

How is the graph of log x - 4 translated from the graph of log x? shifted down 4 units shifted left 4 units shifted right 4 units shifted up 4 units