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.

$\(\frac\)32\(\log\)1$

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\(\ln\)2y-\(\ln\)4x$

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.