document.write( "Question 130626: Solve for x: $\"5%2A6%5E%282x-3%29%2B1=8\"$ \n" ); document.write( "

Algebra.Com's Answer #95396 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"5%2A6%5E%282x-3%29%2B1=8\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"5%2A6%5E%282x-3%29=7\"$ Subtract 1 from both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"6%5E%282x-3%29=7%2F5\"$ Divide both sides by 5\r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%286%5E%282x-3%29%29%29=log%2810%2C%287%2F5%29%29\"$ Take the log of both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x-3%29log%2810%2C%286%29%29=log%2810%2C%287%2F5%29%29\"$ Rewrite the left side using the identity $\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2x-3=log%2810%2C%287%2F5%29%29%2Flog%2810%2C%286%29%29\"$ Divide both sides by $\"log%2810%2C%286%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2x-3=log%286%2C%287%2F5%29%29\"$ Now use the change of base formula to simplify $\"log%2810%2C%287%2F5%29%29%2Flog%2810%2C%286%29%29\"$ to get $\"log%286%2C%287%2F5%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2x=log%286%2C%287%2F5%29%29%2B3\"$ Add 3 to both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%28log%286%2C%287%2F5%29%29%2B3%29%2F2\"$ Divide both sides by 2 to isolate x \n" ); document.write( "

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