Question

Express log base a of x + 1/2log base a of y as a single logarithm.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the rules of logarithms

log $x^{n}$ ⇔ n log x

log x + log y ⇔ log xy

Given

$log_{a}$ x + $\frac{1}{2}$ $log_{a}$ y

= $log_{a}$ x + $log_{a}$ $y^{\frac{1}{2} }$

= $log_{a}$ (x $y^{\frac{1}{2} }$ )

= $log_{a}$ ( x$\sqrt{y}$ )

Answer 2

Answer:  $\bold{log_a(xy^{\frac{1}{2}})}$

Step-by-step explanation:

$log_a(x)+\dfrac{1}{2}log_a(y)\\\\\text{Use the rules for condensing}\\\bullet \text{coefficient becomes exponent}\\\bullet \text{addition becomes multiplication}\\\\.\quad log_a(x)+log_a(y)^{\frac{1}{2}}\\= log_a[(x)(y)^\frac{1}{2}]\\= log_a(xy^{\frac{1}{2}})\\\\\\\text{This can also be written as: }log_a(x\sqrt{y})$