Make p the subject of the equation a^3p= b^(p-1)

Question

Hi, I have an exam on Monday on logarithms and I'm really confused by this question!

In the test I got p/p-1=logb/3loga (this was incorrect)

But today I got  p= logb/(log(b/a^3))

And I don't know if my answer today was right or not, and where I went wrong if it isn't!

Please I would really love some help if you can. Thank you so much!

Answer 1

Take logs of each side:

3plog(a)=(p-1)log(b)=plog(b)-log(b)

p(log(b)-3log(a))=log(b)

p=log(b)/(log(b)-3log(a))=log(b)/log(b/a^3)

So today you got it right!

HINT: If you want to check an answer put in values for the variables.

Let b=256 and a=2. Use logs to base 2.

p=log256/log(256/8)=8/5.

The original equation becomes: 2^(24/5)=256^(3/5)=(2^8)^(3/5)=2^(24/5). So both sides of the equation are equal. This gives you confidence that you found the right answer.