Rational exponents

Question

4^x-3=32

Answer 1

To solve this problem, the first step will be to reduce both constants on either side of the equation to a common base.  In this case, 2 would be a common base for both 4 and 32.

 

4 can be expressed as 2² and 32 can be rewritten as 2⁵ .

Your equation could therefore be expressed as:  2^2(x-3) = 2⁵ .

 

At this point, you would only be solving for x:  2(x -3) = 5 -->  2x - 6 = 5 --> 2x = 11 --> x= 11/2