Question

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.

$5{\log }_{4}x+3{\log }_{4}y$

Short answer

The value is${\log }_4{x}^5{y}^3$

Step-by-step solution

Step 1. Given

An expression is given as$5{\log }_{4}x+3{\log }_{4}y$

Step 2. Calculation

Use property ${\log }_a{M}^p=p{\log }_{a}M$,

$5{\log }_{4}x+3{\log }_{4}y={\log }_4{x}^5+{\log }_4{y}^3$

Now use property ${\log }_{a}M+{\log }_{a}N={\log }_{a}MN$

$5{\log }_{4}x+3{\log }_{4}y={\log }_4{x}^5{y}^3$