physics ques asked: How do you show
log(base 3)3^(2x) = log(base 3) 4
I’m assuming you look at each side separately but not completely sure if someone could show me that would be great thanks
Vincent
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November 11th, 2007 at 1:45 pm
The left hand side involves x, whereas the right hand side does not. Hence, this is not an identity that you prove (”show”), but rather an equation that is to be solved.
Raise both sides to the power of 3 to cancel the log(base3) on both sides.
We have 3^(2x) = 4.
Taking natural logarithms of both sides and dividing over, we have
2x = ln4/ln3
x = ln4/2ln3
November 12th, 2007 at 11:10 pm
log(base 3)3^(2x) = log(base 3) 4
Using the properties of logarithms, pull out the exponents
(2x)(log(base 3)3) = log(base 3) 4
log(base 3) of 3 is 1, so
2x = log(base 3) 4
x = 1/2*log(base 3) 4 = log(base 3) 4^(1/2) = log(base 3) 2