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

1 Answer

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=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.