solve log(x +9) - log x=3
Log [(x+9)/x] = 3
I will assume these are logs to base e.
(x+9)/x = 1 + 9/x = = e^3 = 20.0855..
9/x = 19.0855..
x = 0.47156..
The subject this question is not trigonometry.
If the logs are to base 10, you will get a different answer, but the same method can be used.
To solve the equation log(x + 9) - log x = 3, we can use the properties of logarithms. The property we will use is:
log(a) - log(b) = log(a/b)
Using this property, we can rewrite the equation as:
log((x + 9)/x) = 3
Next, we can rewrite the equation in exponential form:
10^3 = (x + 9)/x
Simplifying further:
1000 = (x + 9)/x
To remove the fraction, we can multiply both sides of the equation by x:
1000x = x + 9
Now, we can solve for x:
1000x - x = 9
999x = 9
x = 9/999
x ≈ 0.009
Therefore, the solution to the equation log(x + 9) - log x = 3 is x ≈ 0.009.