Question

How do you solve `25^x = 5^(x^2 - 15)`?

Answer 1

`x={-3,5}`

Explanation:

`25^x=5^(x^2-15)`

`color(red)(5)^(2x)=color(red)(5)^(x^2-15)`
`"equation has the same base value"`

`2x=x^2-15`

`x^2-2x-15=0`

`(x-5)(x+3)=0`
`if (x-5)=0" then " x=5`
`if(x+3)=0" then "x=-3`
`x={-3,5}`