SOLUTION: log(4)x=2log(4)3

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Question 281925: log(4)x=2log(4)3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C+%28x%29%29+=+2log%284%2C+%283%29%29
With the variable in the argument of a logarithm you will often want to transform the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)

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:
log%284%2C+%28x%29%29+=+log%284%2C+%283%5E2%29%29
or
log%284%2C+%28x%29%29+=+log%284%2C+%289%29%29
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":
x = 9