What is x if #log_4(8x ) - 2 = log_4 (x-1)#?
We would like to have an expression like
- First of all, note that
#4^2=16#, so #2=log_4(16)#.
The equation then rewrites as
But we're still not happy, because we have the difference of two logarithms in the left member, and we want a unique one. So we use
So, the equation becomes
Which is of course
Now we are in the desired form: since the logarithm is injective, if
Which is easily solve into