Question

Use the properties of logarithms to expand the following expression as much as possible. simplify any numerical expressions that can be evaluated without a calculator.
ln(6x9/y5) please show work. the 9 and 5 are both exponents. I don't know how to use this app yet

Answer 1

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y) \\ \quad \\\\ % Logarithm of rationals log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y) \\ \quad \\\\ % Logarithm of exponentials log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\ -----------------------------\\\\ ln\left( \cfrac{6x^9}{y^5} \right)\implies ln(6x^9)-ln(y^5)\implies ln(6)+ln(x^9)-ln(y^5) \\\\\\ ln(6)+9ln(x)-5ln(y)$