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

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

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

simplify

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

ln (\frac{25}{24})

Decimal Notation

0.04082 \dots

Solution steps

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

Apply log rule:

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

2 ln (5) = ln (5^{2})

= - ln (6) + ln (5^{2}) - 2 ln (2)

Apply log rule:

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

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

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

5^{2} = 25

= 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})

(10) lo g_{10} (\frac{2 \cdot 1 0 ^{- 8}}{1 0 ^{- 12}})

\frac{π}{3} ln (2)

- lo g_{10} (9.6 \cdot 1 0^{- 4})

ln ∣ p ∣ - ln ∣ o ∣

lo g_{10} (2 π \cdot 400.2 \cdot 5.03 \cdot 9.566)

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