What is (ln(Δx+x)-ln(x))/(Δx) ?

The solution to (ln(Δx+x)-ln(x))/(Δx) is (ln(Δ+1))/(Δx)

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simplify (ln(Δx+x)-ln(x))/(Δx)

simplify

\frac{ln ( Δ x + x ) - ln ( x )}{Δ x}

\frac{ln ( Δ + 1 )}{Δ x}

Solution steps

\frac{ln ( Δ x + x ) - ln ( x )}{Δ x}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (Δ x + x) - ln (x) = ln (\frac{Δ x + x}{x})

= \frac{ln ( \frac{Δ x + x}{x} )}{Δ x}

Simplify

\frac{Δ x + x}{x} : Δ + 1

= \frac{ln ( Δ + 1 )}{Δ x}

(\frac{1}{54}) ln (\frac{114486}{28000})

ln (\frac{θ}{x ^{θ + 1}})

2 ln (3 t)

4 lo g_{5} (x) + 3 lo g_{5} (y) - 2 lo g_{5} (z)

88.3 + 10 lo g_{10} (\frac{720}{480})

What is (ln(Δx+x)-ln(x))/(Δx) ?
The solution to (ln(Δx+x)-ln(x))/(Δx) is (ln(Δ+1))/(Δx)