Solve : (lg(11/17))^3 = lg(x-7)

Answer 1

In some circles lg(x) means log₂ x
or
you could have just meant log(x).

I will go with the first one ....
(log₂(11/17))^3 = log₂(x-7)
(log(11/17)/log2)^3 = log(x-7)/log2
-.24771... =log(x-7)/.301029...
-.0074568... = log(x-7)
x-7 = 10^-.00745...
x-7 = .84223..

x = 7.84223...

if it were just logs, it is even simpler
(log(11/17) )^3 = log(x-7)
-.006757... = log(x-7)
x-7 = .98456..
x = 7.98456...