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

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Answer 1 · 2016-07-16T07:06:15

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

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. $log_b(4b^2)=2a+2$

Suppose Log_b2=aLog_b2=a and Log_b3=cLog_b3=c, how do you find Log_b(4b^2)Log_b(4b^2)?