Solve the logarithmic equation for x.

log(base 3)(x+6) - log(base 3)(x+1)=1

urgent! help!

To solve the logarithmic equation for x, we can use the properties of logarithms.

The given equation is:
log(base 3)(x+6) - log(base 3)(x+1) = 1

First, we can combine the two logarithms into a single logarithm using the quotient property of logarithms:
log(base 3)((x+6)/(x+1)) = 1

Next, we can rewrite the equation using exponential form:
3^1 = (x+6)/(x+1)

Simplifying the left side gives us:
3 = (x+6)/(x+1)

To eliminate the fraction, we can multiply both sides of the equation by (x+1):
3(x+1) = x + 6

Expanding and simplifying further:
3x + 3 = x + 6

Next, we can rearrange the equation by bringing like terms to one side:
3x - x = 6 - 3

Simplifying both sides gives us:
2x = 3

Finally, we can solve for x by dividing both sides by 2:
x = 3/2

So the solution to the logarithmic equation is x = 3/2.