6. Exponential & Logarithmic Functions

Write each equation in its equivalent logarithmic form. 7^y = 200

Evaluate or simplify each expression without using a calculator. e^{ln 125}

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 (1/5)

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)

Graph each function. ƒ(x) = log₁₀ x

Solve each equation. x = log₃ 1/81

Solve each equation. $x=2^{{\log }_{2}9}$

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

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)

145. Without using a calculator, determine which is the greater number: log₄ 60 or log₃ 40.

Write each equation in its equivalent exponential form. Then solve for x. log₃ (x-1) = 2

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. 3⁴ = 81

Write each equation in its equivalent exponential form. 2 = log₃ x

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

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