Propiedades de los LN

CALCULATIONS INVOLVING LOGARITHMS

Because logarithms are exponents, mathematical operations involving them follow the same rules as those for exponents.

Common Logarithm	Natural Logarithm
log xy = log x + log y	Ln xy = Ln x + Ln y
log x/y = log x - log y	Ln x/y = Ln x - Ln y
log xy = y log x	Ln xy = y Ln x
log y√x = log x1/y = (1/y )log x	Ln y√x = Ln x1/y =(1/y)Ln x

• Example 9: log 5.0 x 10⁶ = log 5.0 + log 10⁶ = 0.70 + 6 = 6.70
  Hint: This is an easy way to estimate the log of a number in scientific notation!
• Example 10: log (154/25) = log 154 - log 25 = 2.188 - 1.40 = 0.788 = 0.79 (2 sig. fig.)
• Example 11: log (5.46 x 10^-3)⁶ = 6 log 5.46 x 10^-3 = 6 x (-2.263) = -13.58
• Example 12: log (4.35)^1/4 = 1/4 log 4.35 = 0.160