What is the limit as x approaches 1+of log_{x}(1/3) ?

The limit as x approaches 1+of log_{x}(1/3) is -1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 1+of log_{x}(1/3)

x \to 1 + lim (lo g_{x} (\frac{1}{3}))

- 1

Solution steps

x \to 1 + lim (lo g_{x} (\frac{1}{3}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= x \to 1 + lim (- lo g_{x} (3))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to 1 + lim (lo g_{x} (3))

Apply the Limit Chain Rule:

1

= - 1

x \to 3 + lim (\frac{1}{x})

x \to 0 lim (cos (x) - cot (x))

x \to - 4 lim (\frac{x + 7}{x + 4})

x \to 3 - lim (x - ∣ x ∣)

x \to a lim (x^{n})

What is the limit as x approaches 1+of log_{x}(1/3) ?
The limit as x approaches 1+of log_{x}(1/3) is -1