The problem presents three logarithmic equations: 1. $\log_4 x = 2$

1. Problem Description

The problem presents three logarithmic equations:

1. $\log_4 x = 2$

2. $\log_5 x = 4$

3. $\log_2 25 = 2$

We are asked to solve for $x$ in the first two equations. The third equation is incorrect, as $\log_2 25 \neq 2$. However, we only need to solve for $x$ in the first two equations.

2. Solution Steps

Equation 1: $\log_4 x = 2$

To solve for $x$, we can rewrite the logarithmic equation in exponential form. The general form is $\log_b a = c \Rightarrow b^c = a$. In this case, we have:

$4^2 = x$

$x = 16$

Equation 2: $\log_5 x = 4$

Similarly, we can rewrite this logarithmic equation in exponential form:

$5^4 = x$

$x = 5 \times 5 \times 5 \times 5$

$x = 25 \times 25$

$x = 625$

3. Final Answer

The solution to the first equation, $\log_4 x = 2$, is $x = 16$.

The solution to the second equation, $\log_5 x = 4$, is $x = 625$.