What is (ln(120)-ln(1200))/(10-1) ?

The solution to (ln(120)-ln(1200))/(10-1) is -(ln(10))/9

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simplify (ln(120)-ln(1200))/(10-1)

simplify

\frac{ln ( 120 ) - ln ( 1200 )}{10 - 1}

- \frac{ln ( 10 )}{9}

Decimal Notation

- 0.25584 \dots

Solution steps

\frac{ln ( 120 ) - ln ( 1200 )}{10 - 1}

Apply log rule:

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

ln (120) - ln (1200) = ln (\frac{120}{1200})

= \frac{ln ( \frac{120}{1200} )}{10 - 1}

Cancel the common factor:

120

= \frac{ln ( \frac{1}{10} )}{10 - 1}

Subtract the numbers:

10 - 1 = 9

= \frac{ln ( \frac{1}{10} )}{9}

Simplify

ln (\frac{1}{10}) : - ln (10)

= \frac{- ln ( 10 )}{9}

Apply the fraction rule:

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

= - \frac{ln ( 10 )}{9}

ln (2) - ln (y) + \frac{1}{2} ln (x + y)

\frac{1}{5} lo g_{6} (b - 6) - \frac{2}{5} lo g_{6} (b)

\frac{1}{4} ln (10) + ln (\frac{13}{4}) - ln (\frac{9}{2})

ln (e^{- w} (e^{- w} - 1))

ln (\frac{3 x - 6}{2 x + 1})

What is (ln(120)-ln(1200))/(10-1) ?
The solution to (ln(120)-ln(1200))/(10-1) is -(ln(10))/9