document.write( "Question 674118: How do I get the solution to
\n" ); document.write( "1/3log(x+2)=log8 \n" ); document.write( "
Algebra.Com's Answer #419037 by swincher4391(1107)\"\" \"About 
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Notice log(a^b) = b*log(a) by our power property of logarithms.\r
\n" ); document.write( "\n" ); document.write( "We have \"%281%2F3%29log%28x%2B2%29\" but that is \"log%28%28%28x%2B2%29%5E%281%2F3%29%29%29\"\r
\n" ); document.write( "\n" ); document.write( "So, \"log%28%28%28x%2B2%29%5E%281%2F3%29%29%29+=+log%288%29\"\r
\n" ); document.write( "\n" ); document.write( "Log is usually noted as base 10, so exponentiate both sides by 10.\r
\n" ); document.write( "\n" ); document.write( "10^log((x+2)^(1/3)) = \"10%5E%28log%288%29%29\" \r
\n" ); document.write( "\n" ); document.write( "\"%28x%2B2%29%5E%281%2F3%29+=+8\"\r
\n" ); document.write( "\n" ); document.write( "Cube both sides.\r
\n" ); document.write( "\n" ); document.write( "\"x%2B2+=+8%5E3\"\r
\n" ); document.write( "\n" ); document.write( "\"x%2B2+=+512\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+510\"\r
\n" ); document.write( "\n" ); document.write( "Check:\r
\n" ); document.write( "\n" ); document.write( "(1/3) * log(510+2) = (1/3) log(512) = .9031\r
\n" ); document.write( "\n" ); document.write( "log(8) = .9031
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