Posted by ted on Tuesday, July 17, 2012 at 3:12pm.
2 log x - log 3 = 2
recall some laws of exponents. Note that we can rewrite the first terms as:
2 log x = log (x^2)
Also, when two log terms of the same base are being subtracted, we can rewrite it as the quotient of the terms inside the log:
log (x^2) - log (3) = log [(x^2)/3]
rewriting the equation,
log (x^2)/3 = 2
we raise both sides by 10 (the base of the log) to cancel the log:
x^2 / 3 = 10^2
x^2 = 300
x = sqrt(300) = +/- 10*sqrt(3)
There are two values of x. But note that we only choose the positive value since we cannot take the log of a negative number (if we substitute back the value of x to the original equation)
Thus, x = 10*sqrt(3)
hope this helps~ :)
yeah it helped. thanks :)
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