Solve each of the following equations. ㏒₇(9x+38) - ㏒₇(x+2) = ㏒₉81

First you need to determine the defined range
(9x + 38) - (x + 2) = (81), x∈ (-2, + ∞)using the (x) - (y) = (), simplify the expression
() =  (81)
write the number in the second set of parenthesis in exponential form
() =   (9²)
using  () = x, simplify the expression
() = 2
the expression (x) = b is equal to x = 
= 7²
evaluate the power
= 49
multiply both sides of the equation by x + 2
9x + 38 = 49(x + 2)
distribute 49 through the parenthesis
9x + 38 = 49x + 98
move the variable to the left side and change its sign
9x - 49x + 38 = 98
move the constant to the right side and change its sign
9x - 49x = 98 - 39
collect the like terms
-40x = 98 - 38
subtract the numbers
-40x = 60
divide both sides of the equation by -40
x = -, x ∈ (-2, + ∞)
finally,, check if the solution is in the defined range
x = -
this means that the correct answer to your question is x = -
let me know if you have any further questions
:)