Question

How do you condense this expression into a single logarithm? `log_(5)x/2+log_(5)y/2+log_(5)z/2`

Answer 1

The Answer is `log_5sqrt(xyz)`.

Explanation:

`(log_5x)/2+(log_5y)/2+(log_5z)/2`.

`=1/2[log_5x+log_5y+log_5z]`.

`=1/2[log_5(x)xx(y)xx(z)]`.

`=1/2log_5xyz`.

`=log_5(xyz)^(1/2)`.

`=log_5sqrt(xyz)`. (Answer).