Question
Asked Oct 23, 2019

logbx=1/2logb9+2/3logb125-logb15

 

Find x.

check_circleExpert Solution
Step 1

Given:

log, (x)log, (9)+log, (125)-log, (15)
3
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log, (x)log, (9)+log, (125)-log, (15) 3

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Step 2

Identity used:

log, (m n)log, (m)+log ,(n)
Identity 1:
Identity 2: log
log, (m)-log, (n)
log, (m*)= nlog, (m)
Identity 3:
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log, (m n)log, (m)+log ,(n) Identity 1: Identity 2: log log, (m)-log, (n) log, (m*)= nlog, (m) Identity 3:

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Step 3

Since,

...
log, (x)log, (9)+log, (125)-log, (15)
(125)-log,(15) dentity 3]
+log
log,(x)= log,9
- log, (15)
log, (x) log, (3)+log,1253
log, (x) log, (3)+log,(5)log, (15)
log, (x)log, (3)+ log, (25)-log, (15)
log, (x)log, (3x 25)- log, (15)
log, (x)log, (75)- log, (15)
[ Identity 1
75
log, (x) log,
Identity2]
15
log, (x)
log, (5)
Taking antilog on both sides,
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log, (x)log, (9)+log, (125)-log, (15) (125)-log,(15) dentity 3] +log log,(x)= log,9 - log, (15) log, (x) log, (3)+log,1253 log, (x) log, (3)+log,(5)log, (15) log, (x)log, (3)+ log, (25)-log, (15) log, (x)log, (3x 25)- log, (15) log, (x)log, (75)- log, (15) [ Identity 1 75 log, (x) log, Identity2] 15 log, (x) log, (5) Taking antilog on both sides,

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