If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
Question 1 Report
If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
Answer Details
To solve the given equation, we can simplify the left-hand side of the equation as follows:
\[\frac{1}{5^{-y}} = 5^y\]
Similarly, we can simplify the right-hand side of the equation as follows:
\[25(5^{4-2y}) = 25 \times 5^4 \times 5^{-2y} = 25 \times 625 \times 5^{-2y} = 15625 \times 5^{-2y}\]
Now we can rewrite the given equation as:
\[5^y = 15625 \times 5^{-2y}\]
Simplifying further, we get:
\[5^{3y} = 15625\]
Taking the cube root of both sides, we get:
\[5^y = 25\]
Thus, y = 2.
Therefore, the value of y is 2. Answer: (b) 2.
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