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Petrovcic2x

Petrovcic2x

Answered question

2022-06-14

Express log 3 5 in terms of p and q
If p = lg 5 and q = log 3 2, express log 3 5 in terms of p and q
Um really confused! How do I solve this?

Answer & Explanation

hildiadau0o

hildiadau0o

Beginner2022-06-15Added 21 answers

Hints:
log 3 5 = lg 5 lg 3
lg 3 = 1 log 3 2
Note: we use above the "change of base" property of logarithms:
log a x = log b x log b a , a , b , x > 0 , a , b 1
Roland Waters

Roland Waters

Beginner2022-06-16Added 6 answers

We have
1 p = 1 log 5 = log 5 10 1 = log 5 2 + log 5 5 = 1 + log 5 2.
Thus
1 p 1 = log 5 2 ,
and hence
= p 1 p = 1 1 p 1 = log 2 5
Finally
log 3 5 = log 3 2 log 2 5 = q p 1 p = p q 1 p .

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