Assessment: Logarithms

What does log_b(x) represent?

When no base is written, "log(x)" is always assumed to mean:

Evaluate log₃(243).

Write 6,200 in scientific notation.

If log_b(5) = 1.16 and log_b(4) = 0.86, find log_b(20). (Round to 2 decimal places.)

Solve for x: log₂(x) = 6.

An earthquake of magnitude 6 releases how many times more energy-related amplitude than a magnitude 4 quake, on the base-10 Richter scale?

Why is the change of base formula needed to evaluate log₆(40) on a typical calculator?

Solve for x: log₄(x) · 3 = 6, i.e. 3 log₄(x) = 6 (find x).

Which value is closest to ln(20), given ln(2) ≈ 0.693 and ln(10) ≈ 2.303?