Question

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

Answer 1

see explanation

Explanation:

Using the rules of logarithms

log
`x^(n)` ⇔ n log x

log x + log y ⇔ log xy

Given

`log_(a)` x +
`(1)/(2)`
`log_(a)` y

=
`log_(a)` x +
`log_(a)`
`y^{(1)/(2) }`

=
`log_(a)` (x
`y^{(1)/(2) }` )

=
`log_(a)` ( x
`√(y)` )

Answer 2

Answer:
`\bold{log_a(xy^{(1)/(2)})}`

Explanation:

`log_a(x)+(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)^{(1)/(2)}\\= log_a[(x)(y)^(1)/(2)]\\= log_a(xy^{(1)/(2)})\\\\\\\text{This can also be written as: }log_a(x√(y))`