What is the limit as x approaches 0 of (2^{3x}-1)/x ?

The limit as x approaches 0 of (2^{3x}-1)/x is 3ln(2)

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limit as x approaches 0 of (2^{3x}-1)/x

x \to 0 lim (\frac{2 ^{3 x} - 1}{x})

3 ln (2)

Decimal Notation

2.07944 \dots

Solution steps

x \to 0 lim (\frac{2 ^{3 x} - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{x}}{1})

= x \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{x}}{1})

Plug in the value

x = 0

= \frac{3 ln ( 2 ) \cdot 8 ^{0}}{1}

Simplify

= 3 ln (2)

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What is the limit as x approaches 0 of (2^{3x}-1)/x ?
The limit as x approaches 0 of (2^{3x}-1)/x is 3ln(2)