Solve the equation $2\log{x} - \log{4} = 2$. We assume the base of the logarithm is 10.

1. Problem Description

Solve the equation $2\log{x} - \log{4} = 2$. We assume the base of the logarithm is

1

0.

2. Solution Steps

First, we can use the logarithm property $n\log{a} = \log{a^n}$ to rewrite the first term:

$2\log{x} = \log{x^2}$

So the equation becomes:

$\log{x^2} - \log{4} = 2$

Next, we use the logarithm property $\log{a} - \log{b} = \log{\frac{a}{b}}$ to combine the terms on the left:

$\log{\frac{x^2}{4}} = 2$

Since the logarithm is base 10, we can rewrite the equation in exponential form:

$\frac{x^2}{4} = 10^2$

$\frac{x^2}{4} = 100$

Multiply both sides by 4:

$x^2 = 400$

Take the square root of both sides:

$x = \pm\sqrt{400}$

$x = \pm 20$

Since the logarithm of a negative number is undefined, we only consider the positive solution.

$x = 20$

3. Final Answer

20