6. Exponential & Logarithmic Functions

Solve each equation. log₂ x = 3

Begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. h(x) = 2 + log₂x

Write each equation in its equivalent logarithmic form. b³ = 1000

Graph f(x) = (1/2)^x and g(x) = log_1/2 x in the same rectangular coordinate system.

Write each equation in its equivalent logarithmic form. ∛8 = 2

Graph each function. Give the domain and range. ƒ(x) = (log_1/2 x) - 2

The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

g(x) = 1-log x

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ √30

Match the function with its graph from choices A–F. ƒ(x) = log₂ x

Evaluate each expression without using a calculator. log₄ 16

Write each equation in its equivalent logarithmic form. 13² = x

Graph f(x) = 4^x and g(x) = log₄ x in the same rectangular coordinate system.

Evaluate each expression without using a calculator. log₅ 5

Solve each equation. log_1/2 (x+3) = -4

Solve each equation. 3x - 15 = log_x 1 (x>0, x≠1)