Question

How do you solve `5^x = 10`?

Answer 1

`x=log_5 10 ~~1.430677`

Explanation:

Make use of the standard relationship
`color(white)("XXX")log_b a = c <=> b^c = a`
or (reversed)
`color(white)("XXX")b^c=a <=> log_b a`

So
`color(white)("XXX")5^x= 10 <=> log_5 10 = x`

`log_5 10` can be evaluated using a calculator as `~~1.430677`