1. ## Expand logarithmic expression

Use the properties of logarithms to expand this expression:
log (12x/7)

Any pointers?

2. Originally Posted by tsmith
Use the properties of logarithms to expand this expression:
log (12x/7)

Any pointers?
First use the property $\displaystyle log(\frac{a}{b})=log(a)-log(b)$ to expand:

$\displaystyle log(\frac{12x}{7})=log(12x)-log(7)$

Then use the property $\displaystyle log(ab)=log(a)+log(b)$ to expand the $\displaystyle log(12x)$ term. The final expression is:

$\displaystyle log(12)+log(x) -log(7)$

Edit, yes you can expand log(12) too as eplained in the reply below.

3. Originally Posted by tsmith
Use the properties of logarithms to expand this expression:
log (12x/7)

Any pointers?
$\displaystyle log_c(ab) = log_c(a) + log_c(b)$

$\displaystyle log_c \left(\frac{a}{b}\right) = log_c(a) - log_c(b)$

If you're asked to simplify log(12) [$\displaystyle log(12) = log(4\cdot 3)$]you'll need the power law: $\displaystyle log_c(a^b) = b\,log_c(a)$

$\displaystyle a,b \neq 0 \: ; \: c \neq 0,1$

Spoiler:
$\displaystyle log(12)+log(x)-log(7) = 2log(2)+log(3)+log(x)+log(7)$