Question

Evaluate the following:

log₆₂₅ 125 + log₆₄ 16

Answer 1

Given: log₆₂₅ 125 + log₆₄ 16

Step-wise calculation:

625 = 5⁴ and 125 = 5³

So `log_625 125 = log_(5^4)` 

`5^3 = 3/4`

64 = 2⁶ and 16 = 2⁴

So `log_64 16 = log_(2^6)`

`2^4 = 4/6`

`2^4 = 2/3`

Sum = `3/4 + 2/3`

= `(9 + 8)/12`

= `17/12`

`17/12` which is `1 5/12 ≈ 1.4167`.