Question

Find the number of solutions for ${\sin }^3(2x+1)=\log \left(x\right)$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

${\sin }^3(2x+1)=\log x$

$x>0$

let $f\left(x\right)=si{n}^3(2x+1)-\log x$

$f\left(x\right)=6{\sin }^2(2x+1)\cos (2x+1)-\frac{1}{x}$

can be positive or negative

so $f\left(0\right)=⇝+\infty$

After certain time $\log x>{\sin }^3(2x+1)$

then $f\left(x\right)$ is negative and remain till $\infty$

so only one time it will be zero

$B$ is correct