For what value of x is the following true?
log(x+4)=logx+log4
logx+log4 = log 4x
so, we want
x+4 = 4x
x = 4/3
To determine the value of x that satisfies the given equation, we can use the properties of logarithms.
The given equation is: log(x+4) = log(x) + log(4)
First, we can simplify the right side of the equation using the logarithmic property that states log(a) + log(b) = log(a*b):
log(x) + log(4) simplifies to log(4x).
Now, our equation becomes: log(x+4) = log(4x)
In order for two logarithms to be equal, the arguments (the values inside the logarithm) must be equal.
So, we have:
x + 4 = 4x
To solve for x, we can bring all the terms to one side:
4x - x = 4
Combining like terms, we get:
3x = 4
Finally, we divide both sides of the equation by 3:
x = 4/3
Therefore, the value of x that satisfies the given equation is x = 4/3.