Question

The number of solutions of ${\log }_3(x-3)=4-x$ is

• A. $0$
• B. $1$
• C. $2$
• D. infinite

Answer 1

Answer: (B)

Given:

${\log }_3(x-3)=4-x$
$\Rightarrow x-3=3^{4-x}$
Let $y=x-3$
$\Rightarrow y=3^4\cdot 3^{-x}$

Lets draw the graphs of $y=x-3$ and $\log x$.

Clearly, from the graph,

The line $y=x-3$ and $\log x$ intersect at only one point $(4,1)$.

So there exist only one solution.

Hence, Option B is correct.