Question

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

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is C, D

To determine which of the given graphs represent the equation \(x^y = 25\), we must identify the relationships that satisfy this equation. For a given \(x, y\), we need \(x^y = 25\). Here's how we can break it down:

1. Rewriting, we have \(y = \log_{x} 25\) which suggests for a fixed x, y is determined such that \(x^y = 25\).
2. Important to note is that this condition implies that both \(x\) and \(y\) need to adapt to satisfy the equation, effectively creating a curve.
3. Analyze graphs to match the behavior defined by \(x^y = 25\), which can display exponential-like curves.

Among the options provided, the graphs in

and

would show sections of these curves where the needed condition \(x^y=25\) is satisfied. Thus, these figures represent the graphs derived from the equation \(x^y = 25\).