Question

The set of all$x$ for which $\log (1+x)\le x$ is :

• A. $(0,\infty )$
• B. $(-1,\infty )$
• C. $(-\infty ,\infty )$
• D. $(1,\infty )$

Answer 1

The correct option is B

$(-1,\infty )$

Explanation for the correct option.

Compute the required value.

Given: $\log (1+x)\le x$

We know that $\log \left(y\right)$ is only defined for, $y\ge 0$.

Thus, $1+x\ge 0$

$\Rightarrow$ $x\ge -1$

Since, $\log \left(x\right)\le 0$ for $x\in \left(0,1\right)$ and $\log \left(x\right)\le x$ for $x\in \left(1,\infty \right)$

therefore, for $\log (1+x)\le x$ solution set is $x\in (-1,\infty )$.

Hence, option (B) is the correct option.