Question

The total number of solution of, $2^x+3^x+4^x-5^x=0$ is(are)

• A. $1$
• B. $2$
• C. $3$
• D. none of these

Answer 1

The correct option is A $1$

The total number of solution of

$2^x+3^x+4^x-5^x=0$ is (are)

Let $f\left(x\right)=5^x$

and $g\left(x\right)=2^x+3^x+4^x$

$f\left(x\right)=5^0=1$

$g\left(0\right)=2^0+3^0+4^0$

$=3$

As f(x) and g(x) are experiential they are

movement

At $x=0$

$f\left(x\right)$ is below $g\left(x\right)$

At $x=3$

$f\left(3\right)=5^3=125$

$g\left(x\right)=2^3+3^3+4^3$

$=8+27+64$

$=99$

Thus f(x) is above g(x)

Thus there exist a solution is $xϵ(0,3)$