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Answer: ["C","D"]

Key insight
The equation x^y = 25 can be rewritten as y = log(25)/log(x) = log₂₅(x)⁻¹. For positive x > 1 it decreases; for 0 < x < 1 it is negative; for x = 5, y = 2; for x = 25, y = 1. It also has a negative branch where y is negative and x is a reciprocal of 5 raised to a negative power.

Step by step
Step 1: Rewrite: y·ln(x) = ln(25), so y = ln(25)/ln(x). This is a hyperbola-like curve in the x-y plane.
Step 2: For x > 1: y decreases from +∞ toward 0 as x increases from 1 to +∞. The curve stays in the first quadrant (positive y, positive x > 1).
Step 3: For 0 < x < 1: ln(x) < 0, so y < 0. The curve passes through the fourth quadrant (positive x, negative y).
Step 4: Check each graph option against these characteristics — the correct ones show the hyperbolic decay in the first quadrant starting from a high y-value near x=1 (options C and D capture the correct portion).
Step 5: Options A and B show curves that don't match the mathematical behaviour of x^y = 25.
Therefore the answer is C and D.

Why wrong options are wrong
Opti

Which of the options show parts of the graph representing the equation x^y = 25?