log5 = 0.699, log2 = 0.301. Use these values to evaluate log40

log5 = 0.699, log2 = 0.301. Use these values to evaluate log40.

One of the logarithmic identities is: log(ab) = log(a) + log(b). Using the numbers 2 and 5, we somehow need to get to 40.

List factors of 40.

On the link above, take a look at the bottom where it says prime factorization. We have:
40 = 2 x 2 x 2 x 5

Using our logarithmic identity, we have:
log40 = log(2 x 2 x 2 x 5)

Rewriting this using our identity, we have:
log40 = log2 + log2 + log2 + log5
log40 = 0.301 + 0.301 + 0.301 + 0.699
log40 = 1.602