Express this logarithm in terms of a and b How do I express log_5 2 in terms of a and b if: log_6 2 =a and log_5 3 =b

Aliyah Thompson

Aliyah Thompson

Answered question

2022-11-11

Express this logarithm in terms of a and b
How do I express log 5 2 in terms of a and b if:
log 6 2 = a and log 5 3 = b
I've tried:
Converting the a and b equations to fractions, and substituting log 2 and log 5 with a log 6 and ( log 3 ) / b respectively, but I ended up with the same equation after simplifying things out.
I've also tried to convert the 2 in log 5 2 into fractions and go from there, but I went up going in circles and never got anywhere.
How would I solve this question?

Answer & Explanation

Phiplyrhypelw0

Phiplyrhypelw0

Beginner2022-11-12Added 24 answers

Using change of base (change to base 5):
log 6 2 = log 5 2 log 5 6 = log 5 2 log 5 3 + log 5 2
a = log 5 2 b + log 5 2
a b = ( 1 a ) log 5 2
log 5 2 = ?
I trust you can finish the rest

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