Question

If log 5 a= 3, then log 5 (a^3) =

Answer 1

There a rule for logarithms:

`\log_n(a^m) = m \cdot \log_n(a)`

So when you're working with
`\log_5(a^3)`, we can use that rule to rewrite this as

`\log_5(a^3) = 3 \cdot \log_5(a)`

And since the first part tells us (on paper) that
`\log_5(a) = 2`, then we can say

`\log_5(a^3) = 3 \cdot \log_5(a) = 3 \cdot 2 = 6`