Logarithm question.. need help badly!!?

Question

Alright, here's the question :

Write the expression as a logarithm of a single quantity --
(It's a lot easier to write this and show a picture)
Here's the link.. http://tinyurl.com/wyvnh
Please show work.. thanks!

Answer 1

alog(x) = log(x^a)

1/4log_b(16) = log_b(16^1/4) = log_b(2)

2log_b(5) = log_b(5^2) = log_b(25)

log_b(7) doesn't change.

log(x) + log(y) = log(xy)

and

log(x) - log(y) = log(x/y)

Therefore

log_b(2)-log_b(25)+log_b(7) = log_b(14/25)

Answer 2

Numbers in front go as exponents; subtraction becomes division; addition becomes multiplication.

So you have log [16^(1/4) x (7) / 5^2]

16^1/4 is 2; 5^2 is 25

so it is log 2x7/25 = log (14/25) [logs are to base b]