Mathematics: What is the solution to log2(2x^3-8)-2log2(x)=log2(x)

What is the solution to log2(2x^3-8)-2log2(x)=log2(x)

Ответ:

clay69

13.03.2022

$\bf \textit{Logarithm of rationals}
\\\\
log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y)
\\\\\\
\textit{Logarithm of exponentials}
\\\\
log_a\left( x^b \right)\implies b\cdot log_a(x)\\\\
-------------------------------$

$\bf log_2(2x^3-8)-2log_2(x)=log_2(x)
\\\\\\
log_2(2x^3-8)-log_2(x^2)=log_2(x)\implies log_2\left( \cfrac{2x^3-8}{x^2} \right)=log_2(x)
\\\\\\
\textit{since both sides are getting }log_2\textit{ we can simply undo that}
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\cfrac{2x^3-8}{x^2}=x\implies 2x^3-8=x^3\implies x^3-8=0
\\\\\\
x^3=8\implies x=\sqrt[3]{8}\implies x=2$

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Ответ:

SmokeyRN

19.09.2020

Mathematics

4th root of a^5b²c^4=ac(4th root of ab²)
ac-7ac=-6ac,
so the result is -6ac(4th root of ab²)

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What is the solution to log2(2x^3-8)-2log2(x)=log2(x)

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