Question

How do I solve 5^3n=125 without using logarithms?

Answer 1

`5^(3n)=125`

`5^(3n)=5^3`

`\implies 3n=3`

Note that this step technically use logarithmic properties, but skips using the language of logarithms by just observing that the bases are the same, so the exponents must also be equal.

Then dividing both sides by 3 gives the solution,
`n=1`.