document.write( "Question 281925: log(4)x=2log(4)3
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Algebra.Com's Answer #205205 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%284%2C+%28x%29%29+=+2log%284%2C+%283%29%29\"$
\n" ); document.write( "With the variable in the argument of a logarithm you will often want to transform the equation into one of the following forms:
\n" ); document.write( "log(expression) = other-expression
\n" ); document.write( "or
\n" ); document.write( "log(expression) = log(other-expression)

\n" ); document.write( "The only difference between your equation and the second form is the 2 in front of the log on the right side. We can't get rid of the 2 by dividing both sides because then the left side would not be right. But we can use the property of logarithms, $\"q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29\"$ , to move the coefficient into the argument as an exponent. Using this property on your equation we get:
\n" ); document.write( " $\"log%284%2C+%28x%29%29+=+log%284%2C+%283%5E2%29%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"log%284%2C+%28x%29%29+=+log%284%2C+%289%29%29\"$
\n" ); document.write( "and we have the second form. With this form we have two logarithms that are equal. The next step is based on some simple logic. If the base 4 log of x is the same as the base 4 log of 9 then x must be the same as 9. In other \"words\":
\n" ); document.write( "x = 9 \n" ); document.write( "

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