write as a single logarithm with a coefficient of 1: 3log(2x)-5log(x)+4log(x)

Question

3log(2x)-5log(x)+4log(x)

Answer 1

First combine the second and third terms:

 

-5log(x)+4log(x) = -log (x)

 

Then use the power rule for logarithms (log a^b = b log a) for the first term:

 

3log(2x) = log (2x)³ = log (8x³)

 

That leaves you with:

 

log (8x³) - log (x)

 

Then use the quotient rule (log (a/b) = log a - log b):

 

log (8x³) - log (x) =

log (8x³ / x) =

log 8x²