loga(x-5)-loga(x+9)=loga(x-7)-loga(x+9)

all the a's are lower

please show work

log [(x-5)/(x+9)]= log[(x-7)/(x+9) ]

(x-5)(x+9) = (x-7)(x+9)

x-5 = x- 7
no solution

x-5/x+9 is equal to x-7/x+9

(x+9 )(x-5) is equal to (x-7)(x+9)
x2-5x+9x -40 equals x2-9x-7x-63
nw solve from there:)

To solve the given equation:

Step 1: Use the property of logarithms that states log(b) - log(c) = log(b/c) for any base a. Apply this property to simplify the equation:

loga((x-5)/(x+9)) = loga((x-7)/(x+9))

Step 2: Since the bases (a) are the same on both sides of the equation, we can eliminate the logarithms by equating the arguments:

(x-5)/(x+9) = (x-7)/(x+9)

Step 3: Now, we can multiply both sides of the equation by (x+9) to get rid of the denominators:

(x-5) = (x-7)

Step 4: Distribute on both sides and simplify:

x - 5 = x - 7

Step 5: Subtract x from both sides to isolate the constant term:

-5 = -7

Step 6: The equation -5 = -7 is not true, which means there isn't a real solution to this equation.