What is 1/(6/7)*ln(1/(1-6/7)) ?

The solution to 1/(6/7)*ln(1/(1-6/7)) is (7ln(7))/6

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simplify 1/(6/7)*ln(1/(1-6/7))

simplify

\frac{1}{\frac{6}{7}} \cdot ln (\frac{1}{1 - \frac{6}{7}})

\frac{7 ln ( 7 )}{6}

Decimal Notation

2.27022 \dots

Solution steps

\frac{1}{\frac{6}{7}} ln (\frac{1}{1 - \frac{6}{7}})

Apply log rule:

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

ln (\frac{1}{1 - \frac{6}{7}}) = ln (1) - ln (1 - \frac{6}{7})

= \frac{1}{\frac{6}{7}} (ln (1) - ln (- \frac{6}{7} + 1))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( ln ( 1 ) - ln ( 1 - \frac{6}{7} ) )}{\frac{6}{7}}

1 \cdot (ln (1) - ln (1 - \frac{6}{7})) = ln (1) - ln (1 - \frac{6}{7})

= \frac{ln ( 1 ) - ln ( - \frac{6}{7} + 1 )}{\frac{6}{7}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{( ln ( 1 ) - ln ( 1 - \frac{6}{7} ) ) \cdot 7}{6}

ln (1) = 0

ln (1 - \frac{6}{7}) = - ln (7)

= \frac{7 ( - ( - ln ( 7 ) ) + 0 )}{6}

Apply rule

- (- a) = a

= \frac{( 0 + ln ( 7 ) ) \cdot 7}{6}

0 + ln (7) = ln (7)

= \frac{7 ln ( 7 )}{6}

ln (x - 3) - ln (x + 3)

5 lo g_{10} (x) + 4 lo g_{10} (y)

\frac{1}{3} ln (6 + 35)

\frac{1}{2} ln ∣ (8.7) + 4 ∣ - \frac{1}{2} ln ∣ (8.7) + 6 ∣ + C

What is 1/(6/7)*ln(1/(1-6/7)) ?
The solution to 1/(6/7)*ln(1/(1-6/7)) is (7ln(7))/6