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ln(2)

10^x = 2

And I get stuck there without a calculator. I could ..

ln(10^x) = ln(2)

x ln(10) = ln(2)

x = ln(2)

But that gets me back to where I started.

So, how would I go about solving 10^x = 2 without a calculator? Using a sort of guessing method, I can't really think of what 10^.1 and 10^.2 would be without going off paper.

I just chose a very basic problem to start with just to get the idea. This is just for myself because I'm curious of learning how to accomplish it. Where this came up was doing things like log(3/2) to find the probability of a (semi) random number starting with 2. I came up with 10^x = 1.5 which wasn't so helpful.

Of course, I plug these into a calculator and get them instantly, but by goal is to do without if it's not extremely difficult.

Thanks