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If \(\log_8 3 = P\) and \(\log_3 5 = Q \), express \(\log_{10} 5\) in terms of \(P\) and \(Q\)

 

The answer isn't supposed to include any logarithms.

 

How should I solve this problem? Thank you in advance!

 Oct 4, 2020
 #1
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P =0.5283208.........

Q =1.4649735.........

P*Q =0.773976......., so:

8^0.773976...... = 5, so:

Log_10(5) = Log_10(8^0.773976...). Remove the "Log"

5 = 8^0.773976 =8^PQ

 

It follows that log_{10} 5 = (P + Q)/(8PQ).

 Oct 4, 2020

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