What is the limit as x approaches 0 of (3^x-5^x)/x ?

The limit as x approaches 0 of (3^x-5^x)/x is ln(3)-ln(5)

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limit as x approaches 0 of (3^x-5^x)/x

x \to 0 lim (\frac{3 ^{x} - 5 ^{x}}{x})

ln (3) - ln (5)

Decimal Notation

- 0.51082 \dots

Solution steps

x \to 0 lim (\frac{3 ^{x} - 5 ^{x}}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 5 ^{x} ln ( 5 )}{1})

= x \to 0 lim (\frac{3 ^{x} ln ( 3 ) - 5 ^{x} ln ( 5 )}{1})

Plug in the value

x = 0

= \frac{3 ^{0} ln ( 3 ) - 5 ^{0} ln ( 5 )}{1}

Simplify

\frac{3 ^{0} ln ( 3 ) - 5 ^{0} ln ( 5 )}{1} : ln (3) - ln (5)

= ln (3) - ln (5)

x \to 2 lim (2 x^{2} - 4 x + 8)

x \to 4 - lim (- \frac{1}{x ^{2} - 16})

x \to 0 lim (x + \frac{x}{x ^{2}})

x \to 0 lim (\frac{( x - 2 )}{x ^{4}})

x \to 2 lim (\frac{[ x ]}{x})

What is the limit as x approaches 0 of (3^x-5^x)/x ?
The limit as x approaches 0 of (3^x-5^x)/x is ln(3)-ln(5)