document.write( "Question 1163250: Pls help me. Given that log2^x+log3^81=1 find x? \n" ); document.write( "
Algebra.Com's Answer #787273 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+log%283%2C%2881%29%29+=+1\"\r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+log%28%2881%29%29%2Flog%28%283%29%29+=+1\" Change of base property. Only change \"log%283%2C%2881%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+log%28%283%5E4%29%29%2Flog%28%283%29%29+=+1\" Rewrite 81 as 3^4\r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+4%2Alog%28%283%29%29%2Flog%28%283%29%29+=+1\" Use the rule that log(x^y) = y*log(x).\r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+4%2Across%28log%28%283%29%29%29%2Fcross%28log%28%283%29%29%29+=+1\"\r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+4%2A1+=+1\" \r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+%2B+4+=+1\" \r
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\n" ); document.write( "\n" ); document.write( "\"log%282%2C%28x%29%29+=+1-4\" Subtracting 4 from both sides\r
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\n" ); document.write( "\"log%282%2C%28x%29%29+=+-3\" \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+2%5E%28-3%29\" Convert from log form to exponent form\r
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\n" ); document.write( "\"x+=+1%2F%282%5E3%29\"\r
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\n" ); document.write( "\"x+=+1%2F8\" is the final answer. This is equivalent to 0.125 in decimal form.
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