Verified answer

3Log₇(1) = 2Log(x-7)

normally when Log has no listed base assume base 10.

given Log(1) of any base is equal to zero.

=> 0 = 2Log(x-7)

given nLog(a) = Log(a^n)

=> 0 = Log((x-7)²)

=> 10^0 = 10^(Log((x -7)²))

=> 1 = (x -7)²

=> x - 7 = ±1

=> x = 7±1

=> x = 6 or 8

Test 2 log (6-7) = 2*Log(-1) isn't a valid function

=> x = 8

=> 2 log (8-7) = 2*Log(1) = 0

=> 3Log₇(1) = 2Log(1) is true.