How to find the x in this exponential function? Thank you!

2(7x+2x1)=7(2x7x1)

1 Answer
May 15, 2018

log3.5(2)

Explanation:

Distributing the variables on each side gives us
27x+22x1=72x77x1

We know ax1a=ax using basic exponent rules, so applying that rule gives us

27x+2x=72x7x
Combine like terms
37x=62x
7x2x=2

Using another exponent rule, we know axb2=(ab)x, so
(72)x=2
3.5x=2

Using logarithms to solve, we arrive at

x=log3.5(2)