SOLUTION: How do you solve the following useing a common base 2^4x-2=32

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Question 412728: How do you solve the following useing a common base
2^4x-2=32
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Please put multiple term exponents in parentheses. What you posted could be interpreted as
2%5E4%2Ax-2+=+32
2%5E%284x%29-2+=+32
or
2%5E%284x-2%29+=+32
Tutors are more likely to help if the problem is clearly stated.

I'm guessing that the last equation is the correct one. If not, you'll have to repost your problem.

When it tells you to use a common base then you should explore powers of the bases you have. You may not have known that 32+=+2%5E5 but it would not take long to find out. Just start raising 2 to various powers. Eventually you would find out that 32 is a power of 2. So we can write your equation with commona bases on each side:
2%5E%284x-2%29+=+2%5E5
The only way for these powers of 2 to be equal is if the exponents themsolves are equal, too. So:
4x-2 = 5
Solving this we get:
x = 7/4