6. Exponential & Logarithmic Functions

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)ln x + ln y

Find each value. If applicable, give an approximation to four decimal places. ln 98/13

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

Write the log expression as a single log.

$\(\log\)_2\(\frac{1}{9x}\)+2\(\log\)_23x$

Use properties of logarithms to rewrite each function, and describe how the graph of the given function compares to the graph of g(x) = ln x. ƒ(x) = ln(e²x)

Let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C. log_b √(2/27)

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(x + 3) - log(2x) = [log(x + 3)/log(2x)]

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log₈ 0.59