# How do you simplify #Log(x+4)=2log(x-2)#?

Simplify the right hand side using the logarithm rule:

Exponentiate both sides, which undoes both logarithms, leaving us with:

Distribute and simplify.

Thus, the only valid answer is

graph{log(x+4)-2log(x-2) [-8.24, 17.07, -3.01, 9.65]}

By signing up, you agree to our Terms of Service and Privacy Policy

To simplify the equation ( \log(x + 4) = 2\log(x - 2) ), we'll first use the properties of logarithms to condense the equation.

[ \log(x + 4) = \log((x - 2)^2) ]

Now, according to the property ( \log_b(a^n) = n\log_b(a) ), we can rewrite ( \log((x - 2)^2) ) as ( 2\log(x - 2) ).

So, the simplified equation becomes:

[ \log(x + 4) = \log((x - 2)^2) ]

Since both sides of the equation are now in terms of the same logarithm, we can drop the logarithms:

[ x + 4 = (x - 2)^2 ]

Next, we expand ( (x - 2)^2 ):

[ x + 4 = x^2 - 4x + 4 ]

Now, we'll move all terms to one side of the equation to solve for ( x ):

[ x - x^2 + 4x - 4 = 0 ]

[ -x^2 + 5x - 4 = 0 ]

Now, we can solve this quadratic equation for ( x ) using factoring, completing the square, or the quadratic formula. Once we find the solutions for ( x ), we can check if they satisfy the original equation.

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7