Question

How do you simplify `log_10(10^3x+1)`?

Answer 1

You can't.

Explanation:

That's as simplified as it gets, unless you mean that you want to convert it to exponential form and solve for `x` (in which case you'd come out with something along the lines of `x = (10^y + 1)/10^3`). If that's what you meant, let me know and I can walk through it.

Or, if you want, you can rewrite it as `log_10(1000x + 1)`, but I wouldn't really call that simplifying.

[I checked WolframAlpha to be more sure.](https://www.wolframalpha.com/input/?i=log_10%20%2810%5E3%20*x%20%2b%201%29)
And then I checked Symbolab.)

Hope this helps.