12^a = 18 & 24^b=16 then find the value of b in terms of a ?

1 Answer

color(blue)(b=(log 8+log 12^a-log 9)/log 24)

with a=log 18/log 12=1.163171163 and b=log 16/log 24=0.8724171679

Explanation:

From the given equations 12^a=18 and 24^b=16
Solution:
From 12^a=18 , we divide both sides of the equation by 9

12^a/9=18/9

12^a/9=2first equation

From 24^b=16, we divide both sides of the equation by 8
24^b/8=16/8

24^b/8=2second equation

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2=2

24^b/8=12^a/9

Multiply both sides by 8

24^b/8=12^a/9

24^b=8*12^a/9

Take the logarithm of both sides of the equation

log 24^b=log 8*12^a/9

b*log 24=log 8+log 12^a-log 9

Divide both sides by log 24

b=(log 8+log 12^a-log 9)/log 24

God bless....I hope the explanation is useful.