Questions: logx(25) = 2 x =

Solution Steps

To solve the equation \(\log_{x}(25) = 2\), we need to convert the logarithmic equation to its exponential form. The equation \(\log_{x}(25) = 2\) is equivalent to \(x^2 = 25\). Solving for \(x\) will give us the value of \(x\).

We start with the equation: \[ \log_{x}(25) = 2 \] This can be rewritten in exponential form as: \[ x^2 = 25 \]

To find \(x\), we take the square root of both sides: \[ x = \sqrt{25} \quad \text{or} \quad x = -\sqrt{25} \] Calculating the square roots gives us: \[ x = 5 \quad \text{or} \quad x = -5 \]

Since the base of a logarithm must be positive and not equal to 1, we discard \(x = -5\) as a valid solution. Thus, the only acceptable solution is: \[ x = 5 \]

Final Answer