Solve for x

Question

2^(3x-2)=4

Answer 1

Note the relationship between log and exponentials:

 

If A = log_X B,  then X^A = B

 

You can say this as follows:

"the log (base X) of B is the power of X required to give B"

 

So, we have:

 

2^(3x -2) = 4

 

therefore:

3x - 2 = log₂4

3x = 2 + log₂4

3x = 2 + 2 = 4

 

x = 4/3

 

CHECK:

 

2^(3(4/3) -2) = 4

2^2 = 4

4 = 4