Question

if (3.7) to the power x = (0.037) to the power y =10000 the ,the value of 1/x-1/y

Answer 1

Answer:

$\frac{1}{x}-\frac{1}{y}=\frac{1}{2}$

Step-by-step explanation:

Given : $3.7^x=0.037^y = 10000$

To Find : $\frac{1}{x}-\frac{1}{y}$

Solution:

$3.7^x=10000$

$x\log_{10}(3.7)=4$

$\frac{\log_{10}(3.7)}{4}=\frac{1}{x}$

Now $0.037^y = 10000$

$y\log_{10}(0.037)=4$

$\frac{\log_{10}(0.037)}{4}=\frac{1}{y}$

So, $\frac{1}{x}-\frac{1}{y}$

$\frac{1}{4}(\log_{10}(3.7)-\log_{10}(0.037))$

$\frac{1}{4}(\log_{10}(\frac{3.7}{0.037}))$

$\frac{1}{4}(\log_{10}(100))$

$\frac{1}{2}$

Hence $\frac{1}{x}-\frac{1}{y}=\frac{1}{2}$

Answer 2

Answer:

0.5 is the correct answer