6. Exponential & Logarithmic Functions

Find the domain of each logarithmic function. f(x) = log₅(x+4)

Evaluate the given logarithm.

$\(\frac\)32\(\log\)1$

Solve each equation. log₄ x = 3

Write each equation in its equivalent exponential form. log₆ 216 = y

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ 6

Evaluate the given logarithm.

$\(\log\)_9\(\frac{1}{81}\)$

Change the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

Evaluate or simplify each expression without using a calculator. 10^{log ∛x}

In Exercises 109–112, find the domain of each logarithmic function. f(x) = ln (x² - 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. h(x) = log x − 1

Graph each function. Give the domain and range. ƒ(x) = (log₂ x) + 3

In Exercises 105–108, evaluate each expression without using a calculator. log (ln e)

Write each equation in its equivalent exponential form. log₃ 81 = y

Evaluate the given logarithm.

$\(\log\)_77^{0.3}$

The figure shows the graph of f(x) = ln x. In Exercises 65–74, 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.

h(x) = ln (2x)