document.write( "Question 763120: Solve for x
\n" ); document.write( "3^(x+4)=27^(2x) \n" ); document.write( "

Algebra.Com's Answer #464498 by DrBeeee(684) $\"\"$ $\"About$

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Given
\n" ); document.write( "(1) $\"3%5E%28x%2B4%29+=+27%5E%282x%29\"$
\n" ); document.write( "Now we know that
\n" ); document.write( "(2) $\"27+=+3%5E3\"$ and apply the rule that when we raise a power by an exponent, we multiply the exponents.
\n" ); document.write( "For example,
\n" ); document.write( "(3) $\"%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29\"$
\n" ); document.write( "In our case we have
\n" ); document.write( "(4) $\"3%5E%28x%2B4%29+=+%283%5E3%29%5E%282%2Ax%29\"$ or
\n" ); document.write( "(5) $\"3%5E%28x%2B4%29+=+3%5E%283%5E%282%2Ax%29%29+\"$ or
\n" ); document.write( "(6) $\"3%5E%28x%2B4%29+=+3%5E%286%2Ax%29\"$
\n" ); document.write( "Now the powers have equal bases on the both sides of (6), so we can equate the exponents and get
\n" ); document.write( "(7) x + 4 = 6x or
\n" ); document.write( "(8) x = 4/5 \n" ); document.write( "

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