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Suppose #Log_b2=a# and #Log_b3=c#, how do you find #Log_b(4b^2)#?

1 Answer

Shwetank Mauria

Jul 16, 2016

#log_b(4b^2)=2a+2#

Explanation:

As #log_b2=a# and #log_b3=c#, we have #b^a=2# and #b^c=3#

Let #log_b(4b^2)=x#, then

#b^x=4b^2=2^2×b^2#

= #(b^a)^2×b^2#

= #b^(2a+2)#

Hence #x=2a+2# i.e. #log_b(4b^2)=2a+2#

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