solve the equation log of base 4 (3x+4) = log of base two (2x+1)
To solve the equation log base 4 (3x + 4) = log base 2 (2x + 1), we need to use the logarithmic properties and convert the equation to a form that allows us to solve for x.
Firstly, we can apply the logarithmic property that states log base a (b) = log base a (c) if and only if b = c.
Therefore, we can rewrite the equation as 3x + 4 = 2x + 1, since both logarithms are equal.
Next, we can simplify the equation by bringing the variables to one side and the constant terms to the other side.
3x - 2x = 1 - 4, or x = -3.
So, the solution to the equation log base 4 (3x + 4) = log base 2 (2x + 1) is x = -3.
well, log_2(n) = 2log_4(n), so you have
log_4(3x+4) = 2log_4(2x+1)
3x+4 = (2x+1)^2
4x^2 + x - 3 = 0
(4x-3)(x+1) = 0
x = 3/4 or -1
But x = -1 does not fit the original equation.