Question 388259: I need help on this question: If Logbase8(3)=p and logbase3(5)=q, express logbase10(5) in terms of p and q.
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! I need help on this question: If Logbase8(3)=p and logbase3(5)=q, express logbase10(5) in terms of p and q.
log8 (3) = p
log3 (5) = q
log written without base is assumed to be log10 normally, writing as log10 to avoid confusion
log10 (5) = ?
logarithmic rule: logb (x) = logk (x) / logk (b) where b is the old base and
k is the new base
log8 (3) = log10 (3) / log10 (8) = p
log3 (5) = log10 (5) / log10 (3) = q
log10 (3) = plog10 (8)
log10 (8) = log10 (3) / p
log10 (5) = qlog10 (3)
log10 (3) = log10 (5) / q and log10 (3) = plog10 (8)
plog10 (8) = log10 (5) / q
pqlog10 (8) = log10 (5)
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