Question

if 5.2 x is equal to 0.52 Y is equal to 10000 then find the value of 1 by x minus 1 by Y

Answer 1

Answer:

$\frac{1}{x}-\frac{1}{y}=0.249$

Step-by-step explanation:

Given : If $5.2^x=0.52^y = 10000$

To find : The value of $\frac{1}{x}-\frac{1}{y}$ ?

Solution :

According to question,

$5.2^x=0.52^y = 10000$

i.e. $5.2^x= 10000$

Taking log both side,

$x\log 5.2=\log 10000$

$x=\frac{\log 10000}{\log 5.2}$

$\frac{1}{x}=\frac{\log 5.2}{\log 10000}$

$\frac{1}{x}=0.179$

Now, $0.52^y= 10000$

Taking log both side,

$y\log 0.52=\log 10000$

$y=\frac{\log 10000}{\log 0.52}$

$\frac{1}{y}=\frac{\log 0.52}{\log 10000}$

$\frac{1}{y}=-0.070$

Substitute the value,

$\frac{1}{x}-\frac{1}{y}=0.179-(-0.070)$

$\frac{1}{x}-\frac{1}{y}=0.179+0.070$

$\frac{1}{x}-\frac{1}{y}=0.249$