Question

If $3^{x/2}+2^x>25$ then the solution set is

• A. $R$
• B. $(2,+\infty )$
• C. $(4,+\infty )$
• D. None of these

Answer 1

The correct option is C $(4,+\infty )$

$3^{\frac{x}{2}}+2^x>25$

$3^{\frac{x}{2}}+4^{\frac{x}{2}}>3^2+4^2$

$f\left(x\right)=3^{\frac{x}{2}}+4^{\frac{x}{2}}$ is a continuously increasing function

since both of them increase with value of x and at $x=4$,$f\left(x\right)=25$

So for all $x>4$,$f\left(x\right)>25$

Hence, option 'C' is correct.