6. Exponential & Logarithmic Functions

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_√19 5

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log_0.1 17

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_1/2 3

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is $1$. $\log 3-3\log x$

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

log_b (xy)⁵ = (log_b x + log_b y)⁵

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log₅ 13

Work each problem. Which of the following is equivalent to 2 ln(3x) for x > 0?

A. ln 9 + ln x

B. ln 6x

C. ln 6 + ln x

D. ln 9x²

Find each value. If applicable, give an approximation to four decimal places. ln 84 - ln 17

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\(\log\)_967$

In Exercises 83–88, let log_b 2 = A and log_b 3 = C and Write each expression in terms of A and C.

log_b (3/2)

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log_√13 12

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. log₃ (7) = 1/[log₇ (3)]

In Exercises 89–102, 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. ln x + ln(2x) = ln(3x)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ 2)