0. Functions

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.

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logb x/y

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logbx²

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logb (√x) / (³√z)

Determine whether the following statements are true and give an explanation or counterexample.

$2=10^{{\log }_{10}2}$