6. Exponential & Logarithmic Functions

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log_π 63

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. log₂ 5

Use a graphing utility and the change-of-base property to graph each function. y = log₃ x

Use a graphing utility and the change-of-base property to graph each function. y = log₂ (x + 2)

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

Expand: $lo{g}_8\left(\frac{4\surd x}{64y3}\right)$

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

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_π e

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 8

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

Solve: log₂ (x+9) — log₂ x = 1.

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

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

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln (b⁴ √a)