6. Exponential & Logarithmic Functions

In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = y

In Exercises 9–20, write each equation in its equivalent logarithmic form. 13^2 = x

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￬4 1/64 = -3

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

In Exercises 21–42, evaluate each expression without using a calculator. log5 (1/5)

Solve each equation. x = 2^log2 9

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

Solve each equation. log￬1/2 (x+3) = -4

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)

Graph f(x) = 4^x and g(x) = log4 x in the same rectangular coordinate system.

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. h(x) = 2 + log2 x

Graph each function. ƒ(x) = log￬1/2 (x+3) - 2

In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log 33)

Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 3/2

In Exercises 81–100, evaluate or simplify each expression without using a calculator. In e^9x

In Exercises 105–108, evaluate each expression without using a calculator. log5 (log7 7)

Without using a calculator, find the exact value of: [log3 81 - log𝝅 1]/[log2√2 8 - log 0.001]