Question

Log4(x+2)-log4(x+3)=-1​

Answer 1

Explanation:

I take it that the base of the log is 4.

So the question can be written as

log_4 [(x+2)/(x + 3)] = -1

If you take the antilog of this, you get

(x + 2)/(x+3) = 4^-1 = 1/4

Now Cross Multiply

4*(x + 2) = 1*(x + 3) Remove the brackets on both sides

4x + 8 = x + 3 subtract x from both sides.

4x - x + 8 = x - x + 3 Combine

3x + 8 = 3 Subtract 8 from both sides

3x = 3 - 8 Combine

3x = - 5 Divide by 3

x = - 5/3