If log10 2 = 0.3010, the value of log10 80 is:

Two logarithm laws apply here: the product rule log(a×b) = log a + log b, and the power rule log(an) = n·log a. Together they let the logarithm of a number be built up from the logarithms of its factors.

1. Factor 80 as a power of 2 times 10: 80 = 23 × 10.

2. Apply the product rule: log1080 = log10(23) + log1010.

3. Apply the power rule to the first term: log10(23) = 3×log102.

4. log1010 = 1, since 10 raised to the power 1 equals 10.

5. Substitute log102 = 0.3010: 3×0.3010 = 0.9030.

6. Add the two parts: 0.9030 + 1 = 1.9030.

Cross-check: log1080 must lie between log1010 = 1 and log10100 = 2, and closer to 2 since 80 is nearer 100 than 10 on a log scale — 1.9030 fits comfortably in that range.