What is 2ln(5)+(-1/5)+3ln(6)-(-2ln(1)-1+3ln(2)) ?

The solution to 2ln(5)+(-1/5)+3ln(6)-(-2ln(1)-1+3ln(2)) is ln(5400)-3ln(2)+4/5

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simplify 2ln(5)+(-1/5)+3ln(6)-(-2ln(1)-1+3ln(2))

simplify

2 ln (5) + (- \frac{1}{5}) + 3 ln (6) - (- 2 ln (1) - 1 + 3 ln (2))

ln (5400) - 3 ln (2) + \frac{4}{5}

Decimal

7.31471 \dots

Solution steps

2 ln (5) + (- \frac{1}{5}) + 3 ln (6) - (- 2 ln (1) - 1 + 3 ln (2))

Apply log rule:

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

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

= ln (5^{2}) + (- \frac{1}{5}) + 3 ln (6) - (3 ln (2) - 2 ln (1) - 1)

Apply log rule:

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

3 ln (6) = ln (6^{3})

= ln (5^{2}) + (- \frac{1}{5}) + ln (6^{3}) - (3 ln (2) - 2 ln (1) - 1)

Apply log rule:

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

ln (5^{2}) + ln (6^{3}) = ln (6^{3} \cdot 5^{2})

= ln (6^{3} \cdot 5^{2}) - \frac{1}{5} - (3 ln (2) - 2 ln (1) - 1)

5^{2} \cdot 6^{3} = 5400

= ln (5400) - \frac{1}{5} - (- 2 ln (1) - 1 + 3 ln (2))

- (- 2 ln (1) - 1 + 3 ln (2)) = - (3 ln (2) - 1)

= ln (5400) - \frac{1}{5} - (3 ln (2) - 1)

- (3 ln (2) - 1) : - 3 ln (2) + 1

= ln (5400) - \frac{1}{5} - 3 ln (2) + 1

Combine the fractions

1 - \frac{1}{5} : \frac{4}{5}

= ln (5400) - 3 ln (2) + \frac{4}{5}

- lo g_{10} (6.656 \cdot 1 0^{- 5})

(\frac{1}{2}) (ln (11 + 22 (6)) - ln (11 - 22 (6)))

\frac{1}{2} lo g_{12} (2)

ln (6 sec (x))

ln ((x y)^{7})

What is 2ln(5)+(-1/5)+3ln(6)-(-2ln(1)-1+3ln(2)) ?
The solution to 2ln(5)+(-1/5)+3ln(6)-(-2ln(1)-1+3ln(2)) is ln(5400)-3ln(2)+4/5