What is simplify-ln(2)+ln(11)-ln(10)-ln(11/5) ?

The solution to simplify-ln(2)+ln(11)-ln(10)-ln(11/5) is -2ln(2)

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simplify-ln(2)+ln(11)-ln(10)-ln(11/5)

simplify

- ln (2) + ln (11) - ln (10) - ln (\frac{11}{5})

- 2 ln (2)

Decimal Notation

- 1.38629 \dots

Solution steps

- ln (2) + ln (11) - ln (10) - ln (\frac{11}{5})

Apply log rule:

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

ln (11) - ln (2) = ln (\frac{11}{2})

= ln (\frac{11}{2}) - ln (10) - ln (\frac{11}{5})

Apply log rule:

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

ln (\frac{11}{2}) - ln (10) = ln (\frac{\frac{11}{2}}{10})

= ln (\frac{\frac{11}{2}}{10}) - ln (\frac{11}{5})

\frac{\frac{11}{2}}{10} = \frac{11}{20}

= ln (\frac{11}{20}) - ln (\frac{11}{5})

Apply log rule:

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

ln (\frac{11}{20}) - ln (\frac{11}{5}) = ln (\frac{\frac{11}{20}}{\frac{11}{5}})

= ln (\frac{\frac{11}{20}}{\frac{11}{5}})

\frac{\frac{11}{20}}{\frac{11}{5}} = \frac{1}{4}

= ln (\frac{1}{4})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= - ln (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{2}) = 2 ln (2)

= - 2 ln (2)

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

0.53 - \frac{0.0591}{2} lo g_{10} (\frac{0.2}{0.9})

lo g_{9} (3 x)

ln (\frac{b}{1 - b}) - ln (\frac{a}{1 - a})

- 0.375 lo g_{2} (0.375) - 0.625 lo g_{2} (0.625)

What is simplify-ln(2)+ln(11)-ln(10)-ln(11/5) ?
The solution to simplify-ln(2)+ln(11)-ln(10)-ln(11/5) is -2ln(2)