Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log. 
$\(\log\)_23789$

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$

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)

Answer each of the following. Write log₃ 12 in terms of natural logarithms using the change-of-base theorem.