Dec 25, 2015 · Exponentiate both sides, which undoes both logarithms, leaving us with: x + 4 = (x −2)2 Distribute and simplify. x + 4 = x2 − 4x + 4 0 = x2 − 5x 0 = x(x − 5) x = 0,5 However, the …

Mar 2, 2018 · However, for x=0, in the original equation, we end up with a log (-4) in the equation. Because, in the domain of real numbers, we are not allowed to have logarithms of negative …

Feb 24, 2016 · log5(x2) = log5(9) Put everything to one side of the equation. 0 = log5(9) −log5(x2) Simplify using the rule logam− logan = loga(m n) 0 = log5(9 x2) Convert to exponential form. …

Apr 11, 2016 · x = 5 Rearrange using laws of logarithms, where a coefficient outside a log is the same as a power inside it. log_8 25 = 2log_8 x = log_8 x^2 Raise both sides by eight, 8^ …

May 21, 2018 · x=sqrt5/10 As 2logx-log5=-2 2logx=-2log10+log5 or logx^2=log(5/10^2) or x^2=5/10^2 or x=sqrt5/10 Observe that though there could have been an answer x=-sqrt5/10 …

Feb 25, 2016 · Note that the solution x=-sqrt14 is invalid, since it would make log (x-2) have a negative argument, and log (a) only exists from a>0. Thus, the only valid solution is x=sqrt14.

Apr 10, 2016 · As logba = loga logb 2log2x − log25 = 22 can be written as 2 logx log2 − log5 log2 = 4 and multiplying each side by log2 as log2 ≠ 0, we get 2logx −log5 = 4log2 or x2 5 = 24 or …

Feb 10, 2017 · 2cot (x) This answer assumes that log (x)=log_e (x), the natural logarithm. First use the rule log (a^b)=blog (a): y=log (sin^2 (x))=2log (sin (x)) From here, we need ...

Sep 11, 2015 · This law allows us to rewrite the left-hand side of the equation as log ( (x + 10)/x) = 2log5. Another law of logarithms, A log B = log B^A, allows us to rewrite the right-hand side …

Jan 23, 2018 · x=4 we need the laws of logs providing all the logs are to the same base log (XY)=logX+logY log (X/Y)=logX-logY logX^n=nlogX we are given 2log_9x=log_9 8+log_9 (x-2) …