Question

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

Answer 1

`\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`