SOLUTION: If log_8 3 = P and log_3 5 = Q, express log_{10} 5 in terms of P and Q. Your answer should no longer include any logarithms.

SOLUTION: If log_8 3 = P and log_3 5 = Q, express log_{10} 5 in terms of P and Q. Your answer should no longer include any logarithms.

Algebra.Com

Question 1177521: If log_8 3 = P and log_3 5 = Q, express log_{10} 5 in terms of P and Q. Your answer should no longer include any logarithms.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Given:

Given those bases and arguments, it is almost certain that we will be working the problem using base 3 logarithms. So

Then

And finally

Simplify/change format if required....

RELATED QUESTIONS
Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your... (answered by greenestamps)

If log(base8) 3=p and log(base3) 5=q, express log(base 10) 5 in terms of p and... (answered by stanbon,Edwin McCravy,Alan3354)

if log 2=p and log 3=q express the following logarithms in terms of p and q 1. log b... (answered by Tatiana_Stebko,lwsshak3)

If log base b of 3 = p and log base b of 5 = q express log base b of 5/b in terms of p... (answered by nerdybill)

Suppose log base b of 3 = p and log base b of 5 = q. Express log base b of 25 in terms... (answered by stanbon)

If log(base 3)2 = P And Log (base 3)13 = Q Express Log(base 78)52 in terms of P and Q (answered by rapaljer)

If p,q>0, log base p of q+ log base qof p=5/2 and pq=54√ 2, then find... (answered by greenestamps)

If log base a =p,log base a=q ,express log base a (6) in term of p and q (answered by ikleyn,greenestamps,josgarithmetic)

Given log 2=p log 7=q Find (14^3x+1)(8^2x+3)=7 in terms of p and... (answered by ikleyn)