To solve this exponential equation, we can first rewrite it using the properties of exponents.
(2^5)^(5-x) = (4/25)^2
Rewrite the left side using the property (a^b)^c = a^(b*c):
2^(5*(5-x)) = (4/25)^2
2^(25-5x) = (4/25)^2
Next, simplify both sides by calculating the exponents:
2^(25-5x) = (16/625)
Next, rewrite the fraction on the right side as a power of 2:
2^(25-5x) = 2^4 / 2^8
Apply the property a^(m)/a^(n) = a^(m-n):
2^(25-5x) = 2^(-4)
Now that the bases are the same, we can set the exponents equal to find the value of x:
25-5x = -4
-5x = -29
x = 29/5
Therefore, the solution to the equation is x = 29/5 or 5.8.
To solve this exponential equation, we can first rewrite it using the properties of exponents.
(2^5)^(5-x) = (4/25)^2
Rewrite the left side using the property (a^b)^c = a^(b*c):
2^(5*(5-x)) = (4/25)^2
2^(25-5x) = (4/25)^2
Next, simplify both sides by calculating the exponents:
2^(25-5x) = (16/625)
Next, rewrite the fraction on the right side as a power of 2:
2^(25-5x) = 2^4 / 2^8
Apply the property a^(m)/a^(n) = a^(m-n):
2^(25-5x) = 2^(-4)
Now that the bases are the same, we can set the exponents equal to find the value of x:
25-5x = -4
-5x = -29
x = 29/5
Therefore, the solution to the equation is x = 29/5 or 5.8.