6. Exponential & Logarithmic Functions

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. g(x) = ln (x+2)

Solve each equation. $x={\log }_8\sqrt[4]{8}$

Find the domain of each logarithmic function. f(x) = ln (x-2)²

Change the following logarithmic expression to its equivalent exponential form.

$\(\log\)_4x=5$

Evaluate or simplify each expression without using a calculator. In e^9x

Write each equation in its equivalent logarithmic form. 2^-4 = 1/16

Write each equation in its equivalent exponential form. 5= log_b 32

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

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. ${\log }_{\sqrt{3}}81=8$

Change the following logarithmic expression to its equivalent exponential form.

$x=\(\log\)9$

Graph each function. ƒ(x) = log₃ (x-1) + 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)

In Exercises 105–108, evaluate each expression without using a calculator. log₅ (log₂ 32)

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)