6. Exponential & Logarithmic Functions

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. $8^{\log_8 19}$

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

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

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

Graph each function. ƒ(x) = log₁₀ x

Graph each function. ƒ(x) = log₆ (x-2)

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. g(x) = log₂ (x + 1)

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)=1+ log₂ x

In Exercises 53-58, 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. g(x) = (1/2)log₂ x