Question 412728
Please put multiple term exponents in parentheses. What you posted could be interpreted as
{{{2^4*x-2 = 32}}}
{{{2^(4x)-2 = 32}}}
or
{{{2^(4x-2) = 32}}}
Tutors are more likely to help if the problem is clearly stated.<br>
I'm guessing that the last equation is the correct one. If not, you'll have to repost your problem.<br>
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 = 2^5}}} 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^(4x-2) = 2^5}}}
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