Question

Expand the logarithmic expression.
log(b)squrt(13/73)

Answer 1

`\log_b\sqrt{(13)/(73)}=\frac12\log_b(13)/(73)=\frac{\log_b13-\log_b73}2`

Answer 2

`\frac{log_b{13}-log_b{73}}{2}`

Explanation:

`log_b{\sqrt{(13)/(73)}}`

First we remove the square root

`log_b({(13)/(73))^(1)/(2)}`

As per log property we can move the exponent 1/2 before log

`(1)/(2)log_b{(13)/(73)}`

Now we apply log property to expand log (13/73)

log(a/b)= log(a) - log(b)

`(1)/(2)log_b{13}-log_b{73}}`

`\frac{log_b{13}-log_b{73}}{2}`