Question

How do you approximate `log_7 36` given `log_7 2=0.3562` and `log_7 3=0.5646`?

Answer 1

Let's first examine the prime factorization of `36`.

`36 = 6 xx 6 = 2 xx 3 xx 2 xx 3 = 2^2 xx 3^2`

So, accordingly, we can write `log_7(36)` as `log_7(2 xx 2 xx 3 xx 3)`, which by the sum rule of logarithms is equal to `log_7(2) + log_7(2) + log_7(3) + log_7(3)`.

This is equal to `0.3562 + 0.3562 + 0.5646 + 0.5646 = 1.8416`

Checking this answer using your calculator, you will find that our answer is quite close to the actual answer, `log_7(36)` having an approximate value of `1.8415644232`.

Hopefully this helps!