Question

$(5.6)^{x} = (0.0056)^{y} = {10}^{5} \: then \: \frac{1}{x} - \frac{1}{y}$


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Answer 1

The answer is 0.6

Step-by-step explanation:

Lets take,

5.6^x = 10^5

x log 5.6 = 5 log 10

x = 5/log 5.6

So, 1/x = log 5.6/5

Now take,

0.0056 ^y = 10^5

y log 0.0056 = 5 log 10

y = 5/ log 0.0056

Then,

1/y = log 0.0056/5

Now, we need to find

1/x - 1/y = log 5.6/5 - log 0.0056/5  

1/x -1/y = log (5.6/0.0056)/5

1/x - 1/y = 3/5 or 0.6

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