6. Exponential & Logarithmic Functions

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?

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)

Find each value. If applicable, give an approximation to four decimal places. log 10¹²

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log₄ (64/y)

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln(e²/5)

Find each value. If applicable, give an approximation to four decimal places. log 0.1

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_b x³

Find each value. If applicable, give an approximation to four decimal places. log 63

Find each value. If applicable, give an approximation to four decimal places. log 0.0022