Rewrite each of the following as an expression of x which does not involve any logs 1000^log(10)(x)

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24-04-2017
Mathematics

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Rewrite each of the following as an expression of x which does not involve any logs 1000^log(10)(x)

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jdoe0001 jdoe0001 · Answer 1 · 2017-04-24T00:59:34+02:00

jdoe0001 jdoe0001

24-04-2017

[tex]\bf 1000^{log_{10}(x)}\qquad 1000=10^3\\\\ -----------------------------\\\\ {{ a}}^{log_{{ a}}x}=x\impliedby \textit{using the log cancellation}\\\\\\ and\qquad log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -----------------------------\\\\ (10^3)^{log_{10}(x)}\implies 10^{3log_{10}(x)}\implies 10^{log_{10}(x^3)}\implies x^3[/tex]

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