What is simplify-ln(6)+ln(5)+ln(5)-2ln(2) ?

The solution to simplify-ln(6)+ln(5)+ln(5)-2ln(2) is ln(25/24)

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simplify-ln(6)+ln(5)+ln(5)-2ln(2)

simplify

- ln (6) + ln (5) + ln (5) - 2 ln (2)

ln (\frac{25}{24})

Decimal Notation

0.04082 \dots

Solution steps

- ln (6) + ln (5) + ln (5) - 2 ln (2)

Apply log rule:

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

ln (5) - ln (6) = ln (\frac{5}{6})

= ln (\frac{5}{6}) + ln (5) - 2 ln (2)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{5}{6}) + ln (5) = ln (5 \cdot \frac{5}{6})

= ln (5 \cdot \frac{5}{6}) - 2 ln (2)

\frac{5}{6} \cdot 5 = \frac{25}{6}

= ln (\frac{25}{6}) - 2 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (\frac{25}{6}) - ln (2^{2})

Apply log rule:

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

ln (\frac{25}{6}) - ln (2^{2}) = ln (\frac{\frac{25}{6}}{2 ^{2}})

= ln (\frac{\frac{25}{6}}{2 ^{2}})

\frac{\frac{25}{6}}{2 ^{2}} = \frac{25}{24}

= ln (\frac{25}{24})

2 ln (5) + 2 ln (2)

ln (- e^{- 2} \cdot 0.2)

lo g_{10} (- 6 i)

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

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

What is simplify-ln(6)+ln(5)+ln(5)-2ln(2) ?
The solution to simplify-ln(6)+ln(5)+ln(5)-2ln(2) is ln(25/24)