document.write( "Question 735095: how do I solve
\n" ); document.write( "10^log base2 x=3 \n" ); document.write( "

Algebra.Com's Answer #449277 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"10%5Elog%282%2C+%28x%29%29=3\"$
\n" ); document.write( "One possible solution:
\n" ); document.write( "Find the base 10 log of each side:
\n" ); document.write( " $\"log%28%2810%5Elog%282%2C+%28x%29%29%29%29=log%28%283%29%29\"$
\n" ); document.write( "Now we can use a property of logarithms, $\"log%28a%2C+%28p%5En%29%29+=+n%2Alog%28a%2C+%28p%29%29\"$ , to rewrite the left side:
\n" ); document.write( " $\"log%282%2C+%28x%29%29%2Alog%28%2810%29%29=log%28%283%29%29\"$
\n" ); document.write( "One of the properties of logarithms you should have learned is:
\n" ); document.write( " $\"log%28a%2C+%28a%29%29+=+1\"$
\n" ); document.write( "So log(10) = 1:
\n" ); document.write( " $\"log%282%2C+%28x%29%29=log%28%283%29%29\"$
\n" ); document.write( "Now we rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+n\"$ is equivalent to $\"p+=+a%5En\"$ . Using this pattern on our equation we get:
\n" ); document.write( " $\"x=2%5Elog%28%283%29%29\"$

\n" ); document.write( "If you want/need a decimal approximation for this answer then just enter the expression on the right side into your calculator. \n" ); document.write( "

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