Simplify logarithms

[justan4cat]

I get most of the way through this one, then I'm stuck. It's multiple choice, and I don't get one of the answers. I don't know what I'm doing wrong.

Express as a single logarithm, and, if possible, simplify.

4 log[sub:wbsuhfsa]a[/sub:wbsuhfsa]y + 1/7 log[sub:wbsuhfsa]a[/sub:wbsuhfsa] z

log[sub:wbsuhfsa]a[/sub:wbsuhfsa] (y z) (4 + 1/7)

 

[Deleted member 4993]

I get most of the way through this one, then I'm stuck. It's multiple choice, and I don't get one of the answers. I don't know what I'm doing wrong.

Express as a single logarithm, and, if possible, simplify.

4 log[sub:3pecdl7i]a[/sub:3pecdl7i]y + 1/7 log[sub:3pecdl7i]a[/sub:3pecdl7i] z

log[sub:3pecdl7i]a[/sub:3pecdl7i] (y z) (4 + 1/7)

\(\displaystyle 4\cdot Log_ay \ \ + \ \ \frac{1}{7}\cdot Log_az\)

\(\displaystyle = \ \ Log_ay^4 \ \ + \ \ Log_az^{\frac{1}{7}}\)

\(\displaystyle = \ \ Log_a\left (y^4 \cdot z^{\frac{1}{7}}\right )\)