Question

How do you solve `log_10y = (1/4)log_10(16) + (1/2)log_10(25)`?

Answer 1

`y = 10`

Explanation:

`log_10 (y) = (1/4) log_10 (16) + (1/2) log_10(25)`

Rules which can be used here.

1. `n*log(a) = log(a^n)`
2. `log(a) + log(b) = log(ab)`
3. If `log(a) = log(b)` then `a=b`

`log_10 (y) = log_10 (16)^(1/4) + log_10 (25)^(1/2)` By rule 1.
`log_10 (y) = log_10 (2) + log_10 (5)` since `a^(1/n) = root(n)a`
`log_10 (y) = log_10 (2*5)` By rule 2.
`log_10 (y) = log_10 (10)`

`y = 10` By Rule 3.

`y = 10` is the final answer.