Use a graphing utility and the change-of-base property to graph each function. y = log₃ x

Use a graphing utility and the change-of-base property to graph each function. y = log₂ (x + 2)

Evaluate or simplify each expression without using a calculator. log 100

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2 log x=log 25

Expand: $lo{g}_8\left(\frac{4\surd x}{64y3}\right)$

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log(x+4)−log 2=log(5x+1)

In Exercises 83–88, let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C.

log_b (3/2)

Evaluate or simplify each expression without using a calculator. log 10⁷

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?

In Exercises 83–88, let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C.

log_b 8

Evaluate or simplify each expression without using a calculator. 10^{log 33}

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2 log x−log 7=log 112

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?

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log x+log(x+3)=log 10

Evaluate or simplify each expression without using a calculator. In 1

Let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C. log_b √(2/27)

Evaluate or simplify each expression without using a calculator. In e

Evaluate or simplify each expression without using a calculator. In e⁶

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. ln(x−4)+ln(x+1)=ln(x−8)

Evaluate or simplify each expression without using a calculator. In (1/e⁶)

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. ln(x−2)−ln(x+3)=ln(x−1)−ln(x+7)

In Exercises 89–102, 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. log₄ (2x³) = 3 log₄ (2x)

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(8x³) = 3 ln (2x)

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

Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

Evaluate or simplify each expression without using a calculator. e^{ln 125}

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

Solve each equation. 5^2x ⋅ 5^4x=125

In Exercises 89–102, 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.

x log 10^x = x²

Solve each equation. 3^x+2 ⋅ 3^x=81