6. Exponential & Logarithmic Functions

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ 3/2

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

In Exercises 105–108, evaluate each expression without using a calculator. log₂ (log₃ 81)

Evaluate each expression without using a calculator. log₂ 64

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. log₃ 27

Without using a calculator, find the exact value of: [log₃ 81 - log_𝝅 1]/[log_2√2 8 - log 0.001]

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

Evaluate each expression without using a calculator. log₂ (1/8)

Solve each equation. $x=3{\log }_{3}8$

Evaluate or simplify each expression without using a calculator. In e⁶

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log16 4

In Exercises 109–112, find the domain of each logarithmic function. f(x) = log[(x+1)/(x-5)]

Evaluate or simplify each expression without using a calculator. log 100