Comments on: Another log problem! Help plz? http://www.about-siding.com/another-log-problem-help-plz/194/ Your Questions, Our Answers Mon, 21 May 2012 04:21:22 +0000 http://wordpress.org/?v=2.2.1 By: Carl L http://www.about-siding.com/another-log-problem-help-plz/194/#comment-279 Carl L Tue, 13 Nov 2007 03:10:00 +0000 http://www.about-siding.com/another-log-problem-help-plz/194/#comment-279 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 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

]]> By: Steven X http://www.about-siding.com/another-log-problem-help-plz/194/#comment-278 Steven X Sun, 11 Nov 2007 17:45:53 +0000 http://www.about-siding.com/another-log-problem-help-plz/194/#comment-278 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 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

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