Solve Log(10^(x))=Log(b^(x)) = 1

[nejnadusho]

I have dilema.

Is there any other solution different than 1?


Log(10^(x))=Log(b^(x)) = 1
...10...b

In words (Log(10^(x))with base 10)=(Log(b^(x))with base b) = 1

And is the second function defines the first one?

Legend
^- on power
=- equals

Thank you guys

 

[Gib Z]

Well have you seen the log identity $$\log_a p^m = m \log_a p$$ where a is any real base? Using that for this thing, the equation simplifies to x= x = 1. So really, no, no other solutions lol.