HELP SOLVE this equation

Question

an earthquake measured 4.2 on the Richter scale. Use the formula R = log(a/a0) to determine approximately how many more times strong the wave amplitude A of the earthquake was than A0

Answer 1

The Richter scale is a logarithmic scale (log base 10),

which means

log(a/a0) = R = 4.2, is the same as

log10(a/a0) = 4.2, so

10^(log10(a/a0)) = 10^4.2, or

a/a0 = 10^4..2, or

a/a0 = 15848.9, or

a/a0 = 16,000 (to 2 significant digits, since R was listed as 4.2)

a = 16,000 * a0. (a is 16,000 stronger than a0), this is the answer