Solve the equation. log(x + 7) – logx = 3
To solve the equation log(x + 7) - logx = 3, we can use the property of logarithms that states log(a) - log(b) = log(a/b).
So, we can rewrite the equation as log((x + 7)/x) = 3.
Now, we can rewrite the equation in exponential form:
(x + 7)/x = 10^3
(x + 7)/x = 1000
Now, we can solve for x by cross multiplying:
x(x + 7) = 1000x
x^2 + 7x = 1000x
x^2 - 993x = 0
x(x - 993) = 0
This gives us two possible solutions:
x = 0 or x = 993
However, since the logarithm of 0 is undefined, the solution x = 0 is extraneous.
Therefore, the only solution to the equation log(x + 7) - logx = 3 is x = 993.