6. Exponential & Logarithmic Functions

Solve each equation. log_x 25 = -2

Evaluate each expression without using a calculator. log₂ (1/√2)

Solve each equation. log₄ x = 3

Solve each equation. log₂ x = 3

Evaluate each expression without using a calculator. log₆₄ 8

Solve each equation. $x={\log }_4\sqrt[3]{16}$

In Exercises 32–35, the graph of a logarithmic function is given. Select the function for each graph from the following options: f(x) = log x, g(x) = log(-x), h(x) = log(2-x), r(x)= 1+log(2-x)

Evaluate each expression without using a calculator. log₅ 5

In Exercises 36–38, begin by graphing f(x) = log2 x Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log2 (x-2)

Evaluate each expression without using a calculator. log₄ 1

Solve each equation. log_1/3 (x+6) = -2

In Exercises 39–40, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = log x and g(x) = - log (x+3)

Evaluate each expression without using a calculator. log₅ 5⁷

In Exercises 39–40, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = ln x and g(x) = - ln (2x)

Evaluate each expression without using a calculator. $8^{\log_8 19}$