There is no any expoent nd power rule... to declare the value of "y".

bt ya.. we can declare the value of 10^-y... infact this one is the ri8 question that u should be to ask !

Understanding the Equation
The equation we have is 10^2y = 25. To solve for y, we need to express both sides in a similar format, preferably using logarithms.
Step 1: Rewrite the Equation
We can rewrite 25 as a power of 10 for easier comparison. We know that:
- 25 can be expressed as 5^2.
So the equation becomes:
- 10^2y = 5^2.
Step 2: Taking Logarithms
To solve for y, we take the logarithm of both sides. We can use the logarithm base 10 or natural logarithm; here we’ll use the logarithm base 10 for simplicity.
- log(10^2y) = log(25).
Using the logarithmic identity log(a^b) = b * log(a), we have:
- 2y * log(10) = log(25).
Since log(10) = 1, this simplifies to:
- 2y = log(25).
Step 3: Finding Log(25)
Next, we need to calculate log(25). We can break it down:
- log(25) = log(5^2) = 2 * log(5).
Thus, we can write:
- 2y = 2 * log(5).
Step 4: Solving for y
Now, we can divide both sides by 2:
- y = log(5).
Conclusion
The value of y is:
- y = log(5).
This represents the logarithm of 5, which can be approximated using a calculator if a numerical value is needed. It provides a clear solution to the original equation by systematically breaking it down using logarithmic principles.