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.

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

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.

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.

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