6. Exponential & Logarithmic Functions

Determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $\(\log\)_6 \(\left\)( \(\frac{x - 1}{x^2 + 4}\) \(\right\)) = \(\log\)_6 (x - 1) - \(\log\)_6 (x^2 + 4)$

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$

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.

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

Answer each of the following. Between what two consecutive integers must log₂ 12 lie?