Question
If $\log (a + 1) = \log (4a - 3) - \log 3;$ find $a.$
✓
Answer
Given that
$\log (a+1)=\log (4 a-3)-\log 3$
$ \Rightarrow \log (a+1)=\log \left(\frac{4 a-3}{3}\right)$
$ \Rightarrow a+1=\frac{4 a-3}{3}$
$ \Rightarrow 3 a+3=4 a-3$
$ \Rightarrow 4 a-3 a=3+3$
$ \Rightarrow a=6$
$\log (a+1)=\log (4 a-3)-\log 3$
$ \Rightarrow \log (a+1)=\log \left(\frac{4 a-3}{3}\right)$
$ \Rightarrow a+1=\frac{4 a-3}{3}$
$ \Rightarrow 3 a+3=4 a-3$
$ \Rightarrow 4 a-3 a=3+3$
$ \Rightarrow a=6$
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