Solve the equation. log(x + 7) – logx = 3
a)3.5
b)142.7
c)0.0070
d)0.0707
To solve this equation, we can use the property of logarithms that states:
log(a) - log(b) = log(a/b)
So, applying this property to the given equation:
log(x + 7) - log(x) = 3
log((x + 7)/x) = 3
Now we can rewrite the equation using exponential form:
10^3 = (x + 7)/x
1000 = (x + 7)/x
Now we can solve for x:
1000x = x + 7
999x = 7
x = 7/999
x = 0.0070
Therefore, the correct answer is:
c) 0.0070