Given that logbase4(y)=a and logbase8(2y)=b, show that 2a=3b-1

How do I go about solving this question?

Question

Given that logbase4(y)=a and logbase8(2y)=b, show that 2a=3b-1

How do I go about solving this question?

zepdrix · Answer

$$\Large\rm \log_4y=a,\qquad \log_8(2y)=b$$Hmm there are a few different ways to get through this one...

anonymous · Answer

the simplest one then, without use of the laws :3

zepdrix · Answer

$$\Large\rm 2(a)=3(b)-1$$$$\Large\rm 2(\log_4 y)=3(\log_8(2y))-1$$That step ok?
I just plugged some stuff in.

Nooooo, definitely using log rules for this one :O

anonymous · Answer

yeap that step's fine

zepdrix · Answer

Mmm I'm trying to think of the continuation that will make the most sense to you.... we're going to have to use some log rules, so it might get a lil tricky.

anonymous · Answer

thing is, this question is in a chapter that hasn't covered the logarithm laws yet, so there should be a way

zepdrix · Answer

Oh ok maybe someone else can help you with that then :)

anonymous · Answer

i mean, the basics have been taught
like not till the multiplication/division part yet
the lny=x thing has been taught

anonymous · Answer

but okay. anyone else? :3

anonymous · Answer

oh wow lolajdsflkfj figured it out