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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.

 Apr 3, 2018
edited by amandapaolars  Apr 3, 2018
 #3
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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)

 Apr 3, 2018
edited by Guest  Apr 3, 2018
 #5
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I get it now sorry

amandapaolars  Apr 3, 2018
edited by amandapaolars  Apr 3, 2018
edited by amandapaolars  Apr 3, 2018
 #6
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+1

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

 Apr 3, 2018
 #7
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can you explain this further with words... I don't get how you got to that conclusion

amandapaolars  Apr 3, 2018
 #8
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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)

 Apr 3, 2018

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