Homework

Problem 1 · easy

Evaluate log_4(64).

Problem 2 · easy

Evaluate log(0.001).

Problem 3 · easy

Evaluate ln(e^5).

Problem 4 · easy

Evaluate e^(ln(7)).

Problem 5 · easy

Write log_5(125) = 3 in exponential form.

Problem 6 · easy

Write 2^(-4) = 1/16 in logarithmic form.

Problem 7 · medium

Expand: ln(x^2 * y^3 / z).

Problem 8 · medium

Expand: log(sqrt(x) / (y * z^2)).

Problem 9 · medium

Condense: 2*log(x) + log(y) - 3*log(z).

Problem 10 · medium

Condense: (1/3)*ln(x) - 2*ln(y).

Problem 11 · medium

Use the change-of-base formula to compute log_7(100) (round to 3 decimal places).

Problem 12 · easy

Solve: log_3(x) = 4.

Problem 13 · easy

Solve: log_2(x + 3) = 5.

Problem 14 · medium

Solve: log(x) + log(x - 1) = log(6).

Problem 15 · medium

Solve: ln(x) = -1.

Problem 16 · medium

Solve: 2*log(x) = log(16).

Problem 17 · medium

Solve: 5^x = 30 (leave answer as ln expression).

Problem 18 · medium

Solve: e^(3x) = 10.

Problem 19 · challenge

Solve: 100 * e^(-0.05t) = 40 for t.

Problem 20 · easy

State the domain of f(x) = log(x - 3).

Problem 21 · medium

State the domain of f(x) = ln(4 - x^2).

Problem 22 · medium

Solve: log_2(x) + log_2(x - 2) = 3.

Problem 23 · medium

What is the vertical asymptote and x-intercept of f(x) = log(x + 5)?

Problem 24 · easy

The pH of a solution is pH = -log[H+]. Find pH when [H+] = 10^(-4).

Problem 25 · challenge

The Richter scale: M = log(I/I_0). An earthquake measures M=6. Another measures M=8. How many times more intense is the M=8 quake?