Question

Simplify the following equation

ln(y) = (3/4)ln(x) + 3

Answer 1

`\bf ln(y)=\cfrac{3}{4}ln(x)+3\\\\ -----------------------------\\\\ recall\\\\ log_{{ a}}\left( (x)/(y)\right)\implies log_{{ a}}(x)-log_{{ a}}(y) \\ \quad \\ % Logarithm of exponentials log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x) \\\\\\ also\qquad a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -----------------------------\\\\ thus \\\\\\`


`\bf ln(y)=ln\left( x^{(3)/(4)} \right)+3\implies ln(y)-ln\left( x^{(3)/(4)} \right)=3 \\\\\\ ln\left( \cfrac{y}{x^{(3)/(4)}} \right)=3\implies ln\left( \cfrac{y}{\sqrt[4]{x^3}}\right)=3`