Solve the equation. log(x + 7) – logx = 3

Answer 1

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.