SOLUTION: Solve for x: log base 4 (x^2 + 3x) - log base 4 (x +5) = 1 I know that I am supposed to do this; 4^1 = x^2 + 3x ----------- -

Question 448342: Solve for x: log base 4 (x^2 + 3x) - log base 4 (x +5) = 1
I know that I am supposed to do this; 4^1 = x^2 + 3x
-------------
x +5
HOwever I am not entirely sure that this is the correct method
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First use the idea that

So the left side should condense into where in this case , and

So the equation simplifies to

Now you can use the property you were referring to and you'll get

Simplify

Multiply both sides by

Distribute.

Get everything to the right side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

However, we need to check them to verify that they are actually solutions. To do so, just plug in the values of x and simplify to get an identity.

It turns out that both solutions check out. So the two solutions are or
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