Question

How do you solve `6^(x+2)=14^(x-3)`?

Answer 1

`x~~13.57`

Explanation:

If `6^(x+2)=14^(x-3)`

then
`color(white)("XX")6^x * 6^2 = 14^x * 1/(14^3)`

`color(white)("XX")(14^x)/(6^x)=6^2 * 14 ^3`

`color(white)("XX")(7/3)^x=98784`

`color(white)("XX")x=log_(7/3) 98784~~13.57357421`
(...and, yes, I used a spreadsheet function to evaluate this)