+72 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.
8^p = 3 and 3^q =5. Sub the first into the 2nd
(8^p)^q = 5
8^pq = 5,
Log_10 (5) =8^(pq)
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
+72 can you explain this further with words... I don't get how you got to that conclusion
Are you having rough day today?
8^p = 3 and 3^q =5.
p =Log(3) / Log(8) =0.52832083357371872715124631464927...........etc.
q =Log(5) / Log(3) =1.4649735207179271671970404076786.............etc.
p*q =0.7739760316291207826234398098298..........etc.
(8^p)^q = 5
8^(p*q) = 8^0.7739760316291207826234398098298.........etc
8^0.7739760316291207826234398098298..... = 5. Sub this for 5 in Log_10(5) and you get
5 = 8^(pq)
