document.write( "Question 414909: there is a question sayins solve for x. and shows 27^2x+1=9^4x
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Algebra.Com's Answer #291021 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
If the equation is
\n" ); document.write( " $\"27%5E%282x%2B1%29+=+9%5E%284x%29\"$
\n" ); document.write( "then please enclose multiple term exponents in parentheses.

\n" ); document.write( "Solving equations where the variable is in an exponent is usually done in one of two ways:

Rewrite both sides as powers of the same number. This cannot be done all the time. But this way is faster/easier when it can be done.
Using logarithms.

\n" ); document.write( "Since 27 and 9 are both powers of 3, the first ways is available to us on this equation:
\n" ); document.write( " $\"%283%5E3%29%5E%282x%2B1%29+=+%283%5E2%29%5E%284x%29\"$
\n" ); document.write( "The rule for exponents when raising a power to a power is to multiply the exponents:
\n" ); document.write( " $\"3%5E%283%2A%282x%2B1%29%29+=+3%5E%282%2A4x%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"3%5E%286x%2B3%29+=+3%5E%288x%29\"$
\n" ); document.write( "This equation now says that two powers of 3 are equal. The only way this can be true is if the exponents are equal, too. So:
\n" ); document.write( "6x+3 = 8x
\n" ); document.write( "This is very easy to solve. Subtracting 6x from each side:
\n" ); document.write( "3 = 2x
\n" ); document.write( "Dividing by 2 we get:
\n" ); document.write( "3/2 = x
\n" ); document.write( "This is the solution to your equation. \n" ); document.write( "

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