College Algebra

Use the compound interest formulas to solve Exercises 10–11. Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. ln e^5

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log16 4

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 (1/5)

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

In Exercises 13–15, write each equation in its equivalent exponential form. log3 81 = y

In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln ∛(x/e)

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 1/2 ln x - ln y

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log 3 - 3 log x

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. e^x=5.7

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2^(4x-2) = 64

In Exercises 74–79, solve each logarithmic equation. log4 (2x+1) = log4 (x-3) + log4 (x+5)

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x

In Exercises 74–79, solve each logarithmic equation. log2 (x+3) + log2 (x-3) =4

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (ln x)(ln 1) = 0

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 8^x = 12143

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x = 7000

n Exercises 92–93, 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 = 6.5(0.43)^x

n Exercises 92–93, 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 = 73(2.6)^x

Use the formula for continuous compounding to solve Exercises 84–85. What annual rate, to the nearest percent, is required for an investment subject to continuous compounding to triple in 5 years?

Use the formula for continuous compounding to solve Exercises 84–85. How long, to the nearest tenth of a year, will it take $50,000 to triple in value at an annual rate of 7.5% compounded continuously?