Question

I need help solving for x: log x = 2.46 - 1.12 * log y

Answer 1

`\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\\\\\ % Logarithm of exponentials log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x) \\\\\\ {{ a}}^{log_{{ a}}x}=x\impliedby \textit{log cancellation rule}\\\\ -----------------------------\\\\`


`\bf log(x)=2.46-1.12log(y)\iff log_(10)(x)=2.46-1.12log_(10)(y) \\\\\\ log_(10)(x)=2.46-log_(10)(y^(1.12))\implies log_(10)(x)+log_(10)(y^(1.12))=2.46 \\\\\\ log_(10)(x\cdot y^(1.12))=2.46\implies 10^{\cfrac{}{}log_(10)(x\cdot y^(1.12))}=10^(2.46) \\\\\\ xy^(1.12)=10^(2.46)\implies \boxed{x=\cfrac{10^(2.46)}{y^(1.12)}}`