Question #26c4a

1 Answer
Nov 28, 2017

Answer:

#x=6#
See explanation.

Explanation:

I assume you mean the following: #81^x = 27^(-x+14)#
So I notice here that #81=9^2=3^4# and that #27=3^3#.
Let's rewrite the equation as such:
#(3^4)^x = (3^3)^(-x+14)#

Then, this becomes:
#3^(4x) = 3^(3(-x+14))#
because exponents of exponents get multiplied.

We can now simplify this by equating just the exponents:
#4x = 3*(-x+14)#

We now simply solve this equation, so opening up the parentheses and keeping simplifying, we get:
#4x = -3x +42#
i.e.
#7x = 42#
i.e.
#x = 6#