What is (ln(5.999)-ln(6))/(5.999-6) ?

The solution to (ln(5.999)-ln(6))/(5.999-6) is -(ln(0.99983…))/(0.001)

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simplify (ln(5.999)-ln(6))/(5.999-6)

simplify

\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}

- \frac{ln ( 0.99983 \dots )}{0.001}

Decimal

0.16668 \dots

Solution steps

\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}

Apply log rule:

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

ln (5.999) - ln (6) = ln (\frac{5.999}{6})

= \frac{ln ( \frac{5.999}{6} )}{5.999 - 6}

Divide the numbers:

\frac{5.999}{6} = 0.99983 \dots

= \frac{ln ( 0.99983 \dots )}{5.999 - 6}

Subtract the numbers:

5.999 - 6 = - 0.001

= \frac{ln ( 0.99983 \dots )}{- 0.001}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{ln ( 0.99983 \dots )}{0.001}

ln (3.5 \cdot 1 0^{- 14})

2 - 0.009 lo g_{10} (\frac{1.3 9 ^{2}}{4.9 3 ^{3}})

lo g_{2} (\frac{4000000}{\frac{1}{65536 \cdot 4000000} \cdot 1})

\frac{1}{3} ln (\frac{91}{30})

- \frac{663 ln ( \frac{13}{133} )}{8}

What is (ln(5.999)-ln(6))/(5.999-6) ?
The solution to (ln(5.999)-ln(6))/(5.999-6) is -(ln(0.99983…))/(0.001)