Logarithm question

[derek916]

28. Expand as much as possible using the properties of logarithms: log ((R/4)^3)


Reading this, it was my understanding I needed to use rules two and three http://www.purplemath.com/modules/logrules.htm

I should be using rule 2) logb(m/n) = logb(m) – logb(n), and 3) logb(m^n) = n · logb(m)

My answer according to these rules would be 3LogR - Log4

However, the answer according to my book is 3LogR + Log4


Is my book wrong? I hope not because I'm studying for an algebra placement test.

[maggiemagnet]

28. Expand as much as possible using the properties of logarithms: log ((R/4)^3)...

My answer according to these rules would be 3LogR - Log4

However, the answer according to my book is 3LogR + Log4

Both answers are wrong!

Since the cube is on the whole fraction, R/4, then the 3 goes out front as:

3*log(R/4)

Then the division turns into subtraction, with the 3 on both:

log(R/4) = log(R) - log(4)

...but the 3 was on the whole log(R/4), not just the "log(R/", so the 3 has to go through the whole thing:

3*[log( ) - log( )]