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.

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

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. 

$\log_23789$

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?