Logarithms, what am I doing wrong ?

Question

If logx=5 , logy=2 and log z= 3 , find the value of log [ (xy^3)/(z) ]?

 

I substituted the numbers inside the brackets then condensed it. I got an answer of 10. But the right answer is 8 apparently? 

Answer 1

Alex,

 

First, you must expand the expression in terms of what you were given.

 

log (xy³/z) = log x + 3 log y − log z  (using properties of logarithms)

 

Now you can plug in the values which were given and simplify the answer:

 

log x + 3 log y − log z = 5 + 3·2 − 3 = 8