6. Exponential & Logarithmic Functions

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

$\(\log\)_841$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₅ (7 × 3)

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_π e

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)

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₇ (7x)

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. ${\log }_4\left(\frac{\sqrt{x}}{64}\right)$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ${\log }_b\left(\frac{\sqrt{x}{y}^3}{z^3}\right)$

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. log₆ [4(x + 1)] = log₆ (4) + log₆ (x + 1)

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

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ${\log }_4\left(\frac{\sqrt{x}}{64}\right)$

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

Find each value. If applicable, give an approximation to four decimal places. ln e^1.6

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\ln \sqrt[5]{x}$

Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984