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
Option A: The curve shape or scale is inconsistent with y = ln(25)/ln(x).
Option B: The starting point or curvature does not match the equation's behaviour near x = 1.

Remember for exam
Always test a few easy values (e.g. x=5 → y=2, x=25 → y=1, x=√5 → y=4) against the graph to verify which options are correct.

c:["3d-geometry","shape-matching","rotation","solid-geometry"] d:["A","D"] b:{"id":"uceed-2022-A220","slug":"uceed-2022-A220","exam":"UCEED","year":2022,"topic":"Spatial Reasoning","tags":"$c","type":"msq","difficulty":"medium","answer":"$d","title":"Shown on the left is a socket with four holes in it. Which of the plugs will fit perfectly in this socket?","searchText":"Shown on the left is a socket with four holes in it. Which of the plugs will fit perfectly in this socket? Spatial Reasoning 3d-geometry shape-matching rotation solid-geometry","paper":"uceed-2022","question_number":20,"section":2,"part":"A"} e:["logical-deduction","calculation","sequence","analogy"] f:["C","D"] 11:["logical-deduction","figure-counting","mathematical-puzzle","seq

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