Set 9: Exponential Functions (Intermediate)

Choice B is correct. Choice B is the correct answer. Rewrite with the same base and solve. 1. Rewrite: $25= 5^2$, so $25\cdot 5^x = 5^2 \cdot 5^x = 5^{x+2}$. 2. Equation: $5^{2 x} = 5^{x+2}$. 3. Equal bases: Set exponents equal: $2x = x + 2$. 4. Solve: $2x - x = 2$, so $x = 2$. 5. Verify: $5^{2(2)} = 5^4 = 625$ and $25\cdot 5^2 = 25 \cdot 25 = 625$ ✓ Strategic Tip: When bases are equal, set exponents equal to solve. Choice A is incorrect because $5^0 = 1$ and $25\cdot 5^0 = 25$, not equal. Choice C is incorrect because $5^2 = 25$ and $25\cdot 5 = 125$, not equal. Choice D is incorrect because $5^{-2} = 0.04$ and $25\cdot 5^{-1} = 5$, not equal.