Evaluating logarithms given log(a)b = 3

[zebra1707]

Hi there

Can someone please review my work and advise.

Homework Statement

Given log(a)b=3 , use the properties of logs to evaluate

4log(a)(1/b)+2log(a)b^3

Homework Equations

I used the rules

log(a)1 = 0

log(a)(x/y) = log(a)x-log(a)y

log(a)x^m = mlog(a)x

The Attempt at a Solution

=4loga1-4logab+2logab^3
=-12+6*3
=-12+18
=6

 

[SammyS]

Hi there

Can someone please review my work and advise.

Homework Statement

Given log(a)b=3 , use the properties of logs to evaluate

4log(a)(1/b)+2log(a)b^3

Homework Equations

I used the rules

log(a)1 = 0

log(a)(x/y) = log(a)x-log(a)y

log(a)x^m = mlog(a)x

The Attempt at a Solution

=4loga1-4logab+2logab^3
=-12+6*3
=-12+18
=6

That is correct !

 

[zebra1707]

That is correct !

Thank you for your assistance.