Question

How do you solve `53^(x + 1) = 65.4`?

Answer 1

`xapprox0.053`

Explanation:

First the the `log` of both sides:
`53^(x+1)=65.4`
`log53^(x+1)=log65.4`
Then because of the rule `loga^b=bloga`, we can simplify and solve:
`(x+1)log53=log65.4`
`xlog53+log53=log65.4`
`xlog53=log65.4-log53`
`x=(log65.4-log53)/log53`
And if you type this into your calculator you get:
`xapprox0.053`