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

1 Answer
Dec 30, 2017

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)