Homework

Problem 1 · easy

Evaluate: 2^5

Problem 2 · easy

Evaluate: (1/3)^3

Problem 3 · easy

Evaluate: log_2(64)

Problem 4 · easy

Evaluate: log_3(1/27)

Problem 5 · easy

Evaluate: log(100)

Problem 6 · easy

Evaluate: ln(e^4)

Problem 7 · easy

Convert to log form: 4^3 = 64

Problem 8 · easy

Convert to exponential form: log_6(36) = 2

Problem 9 · medium

Expand: log(x^3 * y^2)

Problem 10 · medium

Expand: ln(sqrt(x)/y^2)

Problem 11 · medium

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

Problem 12 · medium

Condense: ln(3) + 2*ln(x) - ln(5)

Problem 13 · easy

Solve: 3^x = 81

Problem 14 · easy

Solve: 2^(x+1) = 32

Problem 15 · medium

Solve: 5^x = 12. Round to 3 decimal places.

Problem 16 · medium

Solve: e^(2x) = 7. Round to 3 decimal places.

Problem 17 · medium

Solve: log_3(x + 4) = 3

Problem 18 · medium

Solve: log(5x - 1) = 2

Problem 19 · challenge

Solve: ln(x) + ln(x + 2) = ln(8)

Problem 20 · challenge

$2000 invested at 5% compounded continuously. How long to reach $3000? Round to 2 decimal places.

Problem 21 · easy

Find log_7(49).

Problem 22 · medium

Use the change of base formula to find log_4(20). Round to 3 decimal places.

Problem 23 · challenge

Solve: log_2(x) - log_2(x-1) = 1

Problem 24 · medium

Solve: 4^x = 8

Problem 25 · medium

A radioactive substance has a half-life of 10 years. What fraction remains after 30 years?