Question

If 10^2y =25 is so what is the value of 10^-y

Answer 1

it would be easier to manipulate the original equation 102y = 25 using exponent rules until the lefthand side reads 10-y.

102y = 25

(102y)-1/2= 25-1/2

Recall that when we raise an exponential expression to another exponent, we multiply the exponent values together. In this case, when we multiply 2y*(-1/2) we end up with -y. So now we have:

10-y = 25-1/2

Now, let's rewrite the righthand side so we can simplify it. Recall that x-1 = 1/x and that x1/2 = sqrt(x).

10-y = 1/(251/2)

10-y = 1/sqrt(25)

10-y = 1/5

i hope it will helps you

Answer 2

Answer: 0.2 or 1/5

Step-by-step explanation:

Given that,

$10^{2y}=25$

To solve this question, we have to use log functions. See this example,

$2^{2}=4\\ log_{2} 4= 2$ and

$log_{a}m^{x} =xlog_{a}m$

So, $10^{2y}=25$ can be written as,

$log_{10}25 = 2y$

$log_{10}5^{2} = 2y$

$2log_{10}5=2y$

Divide both sides by 2, we get,

$log_{10}5=y$

Now, writing in exponential form,

$10^{y}=5\\ (10^{y} )^{-1} = 5^{-1}\\ 10^{-y}=\frac{1}{5}\\ 10^{-y}=0.2$