0. Functions

Which of the following lists the correct values for $\ln \left(e\right)$, $\ln \left(e^{2x}\right)$, and $\ln \left(1\right)$, respectively?

1. Express the following logarithms in terms of ln 2 and ln 3.

d. ln ∛9

Evaluate the given logarithm.

$\log_77^{0.3}$

Evaluate the given logarithm.

$\frac32\log1$

Evaluate the given logarithm.

$\log_9\frac{1}{81}$

Write the log expression as a single log.

$\log_2\frac{1}{9x}+2\log_23x$

Write the log expression as a single log.

$\ln\frac{3x}{y}+2\ln2y-\ln4x$

Write the single logarithm as a sum or difference of logs.

$\log_3\left(\frac{\sqrt{x}}{9y^2}\right)$

Write the single logarithm as a sum or difference of logs.

$\log_5\left(\frac{5\left(2x+3\right)^2}{x^3}\right)$

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

$\log_317$

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

$\log_967$

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

$\log_841$

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

$\log_23789$

Evaluate each expression without a calculator.

a. log₁₀ 1000

For a certain constant a>1, ln a≈3.8067 . Find approximate values of  log₂ a and logₐ 2 using the fact that ln 2≈0.6931.