(no roots exist)

R (all real numbers)

{y element R : y>0} (all positive real numbers)

injective (one-to-one)

periodic in x with period (2 i π)/log(10)

1 + x log(10) + 1/2 x^2 log^2(10) + 1/6 x^3 log^3(10) + 1/24 x^4 log^4(10) + O(x^5) (Taylor series)

d/dx(10^x) = 10^x log(10)

integral10^x dx = 10^x/log(10) + constant

lim_(x->-∞) 10^x = 0

10^x = sum_(n=0)^∞ (x^n log^n(10))/(n!)

10^x = sum_(n=0)^∞ ((-1 + x)^n 10 log^n(10))/(n!)

(1 + z)^a = ( integral_(-i ∞ + γ)^(i ∞ + γ) (Γ(s) Γ(-a - s))/z^s ds)/((2 π i) Γ(-a)) for (0<γ<-Re(a) and abs(arg(z))<π)

integral_0^((i π)/log(10)) 10^x dx = -2/log(10)≈-0.868589