Question

Log(x+6)-log(x-3)=1 I need to show work, please show me how

Answer 1

Answer:

x = 4.

Step-by-step explanation:

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

Using the law log a - log b = log a/b:

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

Removing logs:

(x + 6)/ (x - 3) = 10

x+ 6 = 10x - 30

9x = 36

x = 4 (answer).

Answer 2

Answer:

Step-by-step explanation

$log (x+6) - log (x-3) = 1 \\log \frac {x+6}{x-3} = log \ e\\x+6 = e(x-3)\\(1-e)x = -(e+3)\\x=\frac{e+3}{e-1}$

Step 1: on LHS the difference of two logs, is equal of the log of the division, on RHS, 1 is the log of the base, whatever the base is.

Rest is a 1st grade equation, isolate x, divide.