Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.
$\(\log\)_841$

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.

${\log }_5\left(\frac{5{(2x+3)}^2}{x^3}\right)$

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. 

$\(\log\)_23789$

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

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)