What is the limit as x approaches 10^{-4} of ln(x) ?

The limit as x approaches 10^{-4} of ln(x) is -4ln(10)

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limit as x approaches 10^{-4} of ln(x)

x \to 1 0^{- 4} lim (ln (x))

- 4 ln (10)

Decimal

- 9.21034 \dots

Solution steps

x \to 1 0^{- 4} lim (ln (x))

Plug in the value

x = 1 0^{- 4}

= ln (1 0^{- 4})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - 4 ln (10)

What is the limit as x approaches 10^{-4} of ln(x) ?
The limit as x approaches 10^{-4} of ln(x) is -4ln(10)