How do you solve $log (x^{3}) = {(log x)}^{3}$ $log(x^3)=(logx)^3$ ?

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How do you solve $log (x^{3}) = {(log x)}^{3}$ $log(x^3)=(logx)^3$ ?

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Answer 1 · 2015-09-11T06:35:43

x=1, $10^{\sqrt{3}}, 10^{- \sqrt{3}}$ $10^sqrt3, 10^-sqrt3$

Explanation:

$log (x^{3}) = 3 log x$ $log(x^3)= 3log x$

$3 log x = {(log x)}^{3}$ $3log x= (logx)^3$
${(log x)}^{3} - 3 log x = 0$ $(log x)^3 -3logx =0$

$log x ({(log x)}^{2} - 3)$ $logx ( (log x)^2-3)$ =0

logx=0, ${(log x)}^{2} - 3 = 0$ $(logx)^2 -3=0$

log x=0 means x=1 and ${(log x)}^{2} - 3 = 0$ $(logx )^2 -3=0$ would mean $log x = \pm \sqrt{3}$ $log x=+-sqrt3$ , or $x = 10^{\sqrt{3}}, 10^{- \sqrt{3}}$ $x=10^sqrt3, 10^-sqrt3$

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How do you solve $log (x^{3}) = {(log x)}^{3}$ $log(x^3)=(logx)^3$ ?

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How do you solve $log (x^{3}) = {(log x)}^{3}$ $log(x^3)=(logx)^3$ ?