Question

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

Answer 1

`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=2`first equation

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

`24^b/8=2`second equation

~~~~~~~~~~~~~~~~~~~~~~~~~

`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.