Question

find the value
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Answer 1

Answer:

1/5 Mark me as brainlieast and follow me

Answer 2

10^(2y) = 25

Since the base is 10, we can write,

log (25) = 2y

=> log (5^2) = 2y

=> 2 log (5) = 2y

=> log (5) = y

=> - log (5) = - y

=> log (5^(-1)) = - y

=> log (1/5) = - y

From this, we get that,

10^(- y) = 1/5

Hence 1/5 is the answer.

Here I used only one identity.

log(x^a) = a · log (x)

And conversely,

a · log (x) = log (x^a)

Or, we can find the answer without using logarithm!

10^(2y) = 25

=> (10^y)^2 = 5^2

=> 10^y = 5

Now, since 10^(2y) = 25 is given, divide LHS by 10^(2y) and RHS by 25. So,

(10^y) ÷ (10^(2y)) = 5 ÷ 25

=> 10^(y - 2y) = 1/5

=> 10^(- y) = 1/5

So we got the answer. We can find out the answer by this too.