Make sure you write the question well.
The solution to what you wrote is:
log x - log x -12 = 2 log ( x - 1 )
- 12 = 2 log ( x - 1 )
Divide both sides by 2
- 6 = log ( x - 1 )
log ( x - 1 ) = - 6
If your logarithm is the logarithm with base 10:
10^ [ log ( x - 1 ) ] = 10^ - 6
x - 1 = 0.000001
Add 1 to both sides
x = 1.000001
Find the solution of the equation , log 𝑥 − log 𝑥 − 1
2 = 2 log( 𝑥 − 1)
2 answers
Since the equation makes no sense as written,
maybe you meant
log 𝑥 − (log 𝑥 − 12) = 2 log( 𝑥 − 1)
x = 1 + 10^6
Or maybe you meant
log x − log (x − 1)/2 = 2 log( x − 1)
Probably not, since that is equivalent to
(x-1)^3 = 2x
oh, well...
maybe you meant
log 𝑥 − (log 𝑥 − 12) = 2 log( 𝑥 − 1)
x = 1 + 10^6
Or maybe you meant
log x − log (x − 1)/2 = 2 log( x − 1)
Probably not, since that is equivalent to
(x-1)^3 = 2x
oh, well...