How to Evaluate Logarithms the Easy Way Without a Calculator

Evaluate logarithms involving radicals, negative exponents, fractional exponents.
Apply the one-to-one property of exponential functions.
Evaluate Common and Natural Logarithms.

[contemporarilyancient]

Log4(16) = n
4ⁿ = 4²
n = 2

Log4(1) = n
4ⁿ = 4⁰
n = 0

Log4(1/16) = n
4ⁿ = 4^-2
n = -2

Log4(8) = n
4ⁿ = 8
2²ⁿ = 2³
2n = 3
n = 3/2

Log9(sqrt3) = n
9ⁿ = 3^½
3²ⁿ = 3^½
2n = ½
n = ¼

Log5(sqrt5) = n
5ⁿ = 5^½
n = ½

Log(1000) = n
10ⁿ = 10³
n = 3

Log(0.1) / n
10ⁿ = 10^-1
n = -1

ln(1) = n
eⁿ = e⁰
n = 0

Answers : 2; 0; -2; 3/2; 1/4; 1/2; 3; -1; 0.