How to express as a single logarithm & simplify (12)loga⋅x+4loga⋅y−3loga⋅x?

Bradyn Mclean

Bradyn Mclean

Answered

2022-12-31

How to express as a single logarithm & simplify (12)logax+4logay3logax?

Answer & Explanation

possetzvjm

possetzvjm

Expert

2023-01-01Added 4 answers

You must employ the following logarithm properties in order to make this expression simpler:
log(ab)=log(a)+log(b) (1)
log(ab)=log(a)log(b) (2)
log(ab)=blog(a) (3)
Using the property (3), you have:
(12)loga(x)+4loga(y)3loga(x)=loga(x12)+loga(y4)loga(x3)
Then, using the properties (1) and (2), you have:
loga(x12)+loga(y4)loga(x3)=loga(x12y4x3)
Then, you only need to put all the powers of x
together:
loga(x12y4x3)=loga(x52y4)

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