document.write( "Question 412728: How do you solve the following useing a common base
\n" ); document.write( "2^4x-2=32 \n" ); document.write( "

Algebra.Com's Answer #289832 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Please put multiple term exponents in parentheses. What you posted could be interpreted as
\n" ); document.write( " $\"2%5E4%2Ax-2+=+32\"$
\n" ); document.write( " $\"2%5E%284x%29-2+=+32\"$
\n" ); document.write( "or
\n" ); document.write( " $\"2%5E%284x-2%29+=+32\"$
\n" ); document.write( "Tutors are more likely to help if the problem is clearly stated.

\n" ); document.write( "I'm guessing that the last equation is the correct one. If not, you'll have to repost your problem.

\n" ); document.write( "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:
\n" ); document.write( " $\"2%5E%284x-2%29+=+2%5E5\"$
\n" ); document.write( "The only way for these powers of 2 to be equal is if the exponents themsolves are equal, too. So:
\n" ); document.write( "4x-2 = 5
\n" ); document.write( "Solving this we get:
\n" ); document.write( "x = 7/4 \n" ); document.write( "

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