document.write( "Question 736028: Solve for x:log 16 base x÷log x base 16=3 \n" ); document.write( "

Algebra.Com's Answer #450140 by lwsshak3(11628) $\"\"$ $\"About$

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Solve for x:log 16 base x÷log x base 16=3
\n" ); document.write( " $\"log%28x%2C%2816%29%29%2Flog%2816%2C%28x%29%29=%283%29\"$
\n" ); document.write( "Convert to base(10)
\n" ); document.write( " $\"%28log%2816%29%2Flog%28x%29%29%2F%28log%28x%29%2Flog%2816%29%29=%283%29\"$
\n" ); document.write( " $\"%28%28log%2816%29%29%5E2%29%2F%28%28log%28x%29%29%5E2%29=%283%29%29\"$
\n" ); document.write( "take sqrt of both sides:
\n" ); document.write( " $\"%28log%2816%29%29%2F%28log%28x%29%29=sqrt%283%29%29\"$
\n" ); document.write( "log(16)=√3log(x)
\n" ); document.write( "log(x)=log(16)/√3≈0.6952
\n" ); document.write( "x=10^0.6962≈4.9568
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "log(16) basex≈1.732
\n" ); document.write( "logx base(16)≈0.5773
\n" ); document.write( "(1.732/0.5773≈2.999..≈3
\n" ); document.write( " \n" ); document.write( "

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