Question #a6ad5

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Question #a6ad5

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Answer 1 · 2017-07-19T18:33:55

$x = 2$ $x=2$

Explanation:

$\frac{log 2 x}{1 - log 5} = 2 \Leftrightarrow log 2 x = 2 - 2 log 5 \Leftrightarrow$ $(log2x)/(1-log5)=2 iff log2x=2-2log5 iff$

$log 2 x = {log 10}^{2} - {log 5}^{2} \Leftrightarrow log 2 x = log (\frac{10^{2}}{5^{2}}) \Leftrightarrow$ $log2x=log10^2-log5^2iff log2x=log(10^2/5^2)iff$

$2 x = \frac{100}{25} \Leftrightarrow 2 x = 4 \Leftrightarrow x = 2$ $2x=100/25iff2x=4iffx=2$

Answer 2 · 2017-07-19T19:24:02

$x = 2$ $x=2$

Explanation:

$note that log x \equiv {log}_{10} x$ $"note that "logx-=log_(10)x$

$log 2 x = 2 (1 - log 5) = 2 - 2 log 5$ $log2x=2(1-log5)=2-2log5$

$\Rightarrow log 2 x = log 100 - log 25 \leftarrow {log}_{10} 100 = 2$ $rArrlog2x=log100-log25larr log_(10)100=2$

$\Rightarrow log 2 x = log (\frac{100}{25}) = log 4$ $rArrlog2x=log(100/25)=log4$

$\Rightarrow 2 x = 4 \Rightarrow x = 2$ $rArr2x=4rArrx=2$

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