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

1 Answer
Alan P.
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)

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