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

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

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

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

ln (5) - ln (3)

Decimal Notation

0.51082 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

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

= ln (5) - ln (3)

f^{^{'}} (a) = 2

\frac{d y}{d x} = (\frac{x e ^{x}}{y 9 + y ^{2}})

\int (3 x) d x

\int x (x^{2} + 6)^{4} d x

n = 1 \sum \infty \frac{n}{e ^{3 n}}

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