What is ((ln(x+h)-ln(x)))/h ?

The solution to ((ln(x+h)-ln(x)))/h is (ln((x+h)/x))/(h)

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simplify ((ln(x+h)-ln(x)))/h

simplify

\frac{( ln ( x + h ) - ln ( x ) )}{h}

\frac{ln ( \frac{x + h}{x} )}{h}

Solution steps

\frac{( ln ( x + h ) - ln ( x ) )}{h}

Apply log rule:

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

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

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

lo g_{b} (\frac{3}{4})

lo g_{10} (\frac{85347 \cdot 15274}{125386})

lo g_{3} (\frac{x}{27})

lo g_{10} (0.1) + lo g_{10} (0.01)

ln (x) + ln (2 x + 5)

What is ((ln(x+h)-ln(x)))/h ?
The solution to ((ln(x+h)-ln(x)))/h is (ln((x+h)/x))/(h)