This math question confused 97% of examinees | Be Careful! 

For the 2nd root, we can choose for the branch cut of the logarithm in the complex plane one that's not on the half-line of non-positive reals. E.g., choose the branch cut on the upper imaginary line such that the argument of a complex number, θ, satisfies -3π/2

Should mention that x=log ф

as early as possible, set if we are working in Real or Complex

Answer x = log 1.61803 or 0.2089 or 0.21 This is the golden ratio 1^x + 10^ x =100^x 1 + 10^x = 100^x (since 1^ any number = 1) 0= 100^x - 10^x -1 let 10^x = p Hence, 0= p^2 - p -1 Using the quadratic formulae and p = (1 + or -sqrt 5 )/2 or 1.61803 or -0.61803 Golden ratio Hence, 10^x = 1.61803 as you find the log a negative number, so disregard - 0.61803 x log 10 = log 1.61803 find the log of both sides x = log 1.61803 or 0.2089865693 Answer

And once again the golden ratio shows up 😉

So whatdowehaverighthere😂…

By inspection my guess was .2, but knew their were more trailing digits. Watched your solution and by slide rule .209

I solved this problem really 😎 without watching this video.

thanks for your lesson! The explanation is detailed and clear. Where can I see more of your lessons on other topics? Thank you in advance and good luck with everything.

Answer is ln(phi) / ln(10) That's what I got.

I reckon it's going to have to do with phi... Curious one