exponential equation 23x = 6

Question

Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

Answer 1

I'm guessing you meant 2^3x = 6.  To solve this equation means to find the value of x that makes it true, so you want to end up with x = something.  The x is stuck up in the exponent, so we need to get it down from there.  We do that by using logs, in this case we'll use log base 2 because the base of the exponent is 2.  So take the log base 2 of both sides to eliminate the exponent then solve for x.

 

2^3x = 6

log₂(2^3x) = log₂(6)

3x = log₂(6)

x = (1/3)log₂(6) ≅ 0.862 ...