Solve the logarithmic equation.
log2(4x)-log2(x+3)=1
log2(4x - log2(x+3) = 1
log2(4x/(x+3)) = 1
4x/(x+3) = 2^1 = 2
4x = 2x+6
2x = 6
x = 3
Thanks for your help!! I knew how to start, just wasn't sure the steps to go!
To solve the logarithmic equation log2(4x) - log2(x + 3) = 1, we can use the logarithmic properties to simplify it.
First, let's apply the quotient property of logarithms, which states that log a - log b = log(a / b).
Using this property, we can rewrite the equation as log2((4x) / (x + 3)) = 1.
Next, we can convert the logarithmic form into exponential form. In general, if log_a(x) = b, then a^b = x.
Applying this exponential form, we have 2^1 = (4x) / (x + 3).
Simplifying the equation further, we get 2 = (4x) / (x + 3).
To eliminate the fraction, we can cross-multiply: 2(x + 3) = 4x.
Expanding the equation, we have 2x + 6 = 4x.
Now, let's solve for x:
Subtracting 2x from both sides, we get 6 = 2x.
Dividing both sides by 2, we have x = 3.
Therefore, the solution to the logarithmic equation log2(4x) - log2(x + 3) = 1 is x = 3.