Question

The number of values of $x$ satisfying the equation $2^{{\log }_{5}16.{\log }_{4}x+{\log }_{x\sqrt{2}}5}+5^x+x^{{\log }_{3}4+5}+x^5=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

According to the given equation the value of $x$ can not be negative and also not zero such that $x\in R^{+}$

For these values of $x$, each term at left is positive as

$2^{{\log }_{5}16\cdot {\log }_{4}x+{\log }_{x\sqrt{2}}5}$ is exponent function and always positive

$5^x$ is exponent function and always positive

$x^{{\log }_{3}4+5}$ is always positive for $x\in R^{+}$

$x^5$ is always positive for $x\in R^{+}$

Hence, no value of $x$ such that the equation result is zero.