Determine logarithm versus known values of $ a,b$

Question

We know $\log_{30}(3)=a, \log_{30}(5)=b.$ How to determine $\log_{30}(16)$?

Are you sure it shouldn't be $15$ instead of $16$? – Bobson Dugnutt Feb 13 '16 at 17:36 — Bobson Dugnutt, Feb 13 '16 at 17:36

score 5 · Accepted Answer · answered Feb 13 '16 at 17:40

5

For convenience we'll denote $log_{30}$ by $log$.

We note that $$1=log(30)=log(6\times 5)=log(6)+log(5)=log(6)+b\implies log(6)=1-b$$

But then we have $$1-b=log(6)=log(2\times 3)=log(2)+log(3)=log(2)+a\implies log(2)=1-b-a$$

Can you finish from here?

answered Feb 13 '16 at 17:40

lulu

1 Answers1