Question

If $x=500,y=100$ and $z=5050$, then the value of $\left({\log }_{xyz}{x}^z\right)(1+{\log }_{x}yz)$ is equal to.

• A. 500
• B. 100
• C. 5050
• D. 10

Answer 1

The correct option is C 5050

Given,

$\left({\log }_{xyz}\left(x^z\right)\right)(1+{\log }_x\left(yz\right))$

$\left({\log }_{xyz}\left(x^z\right)\right)(1+{\log }_x\left(yz\right))$

$=z{\log }_{xzy}\left(x\right)({\log }_x\left(zy\right)+1)$

from given w have,

$=5050{\log }_{(500\times 5050\times 100)}\left(500\right)({\log }_{500}\left(\right(5050\times 100\left)\right)+1)$

$=\frac{5050{\log }_e\left(505000\right)}{{\log }_e\left(252500000\right)}+5050{\log }_{252500000}\left(500\right)$

$=5050$