1. ## Logs

Express each of the following in terms of log a and log b:

(1) 1/2 log 80 - 1/2 log 5

(2) 2 log a -log b - log c

(3) log 15 - 1/2 log a

(4) log base2 - log 3 + log 5

2. Not really sure if the question links well with the problems

for the first one you can factor out the half in each term then use the identity for subtracting logs

i.e. $\displaystyle \displaystyle \log a - \log b = \log \frac{a}{b}$

3. Here is a suggestion:
$\displaystyle \begin{array}{rcl} {\log (80)} & = & {\log (10) + \log (8)} \\ {} & = & {\log (10) + 3\log (2)} \\ {} & = & {4\log (2) + \log (5)} \\ \end{array}$

4. Without knowing what a, b, and c are, or at least what log(a) and log(b) are, I cannot imagine how you could write
"(1/2)log(80)- (1/2)log(5)" "in terms of log(a) and log(b)".

It is certainly true that (1/2)log(80)- (1/2)log(5)= (1/2)log(80/5)= (1/2)log(16)= log(4) but, again, how is that connected to a and b?

5. ## logs

Hi renii.
Is the question simplify these logs? If so 1 = log 4 and 2 log a^2/bc

bjh