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

The solution to simplify-2ln(6)-ln(5)+ln(3)+2ln(2) is -ln(15)

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

simplify

- 2 ln (6) - ln (5) + ln (3) + 2 ln (2)

- ln (15)

Decimal Notation

- 2.70805 \dots

Solution steps

- 2 ln (6) - ln (5) + ln (3) + 2 ln (2)

Apply log rule:

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

2 ln (6) = ln (6^{2})

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

Rewrite

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

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

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

Apply log rule:

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

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

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

6^{2} \cdot 5 = 180

= - ln (180) + ln (3) + 2 ln (2)

Apply log rule:

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

ln (3) - ln (180) = ln (\frac{3}{180})

= ln (\frac{3}{180}) + 2 ln (2)

Cancel the common factor:

3

= ln (\frac{1}{60}) + 2 ln (2)

Apply log rule:

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

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

= ln (\frac{1}{60}) + ln (2^{2})

Apply log rule:

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

ln (\frac{1}{60}) + ln (2^{2}) = ln (2^{2} \cdot \frac{1}{60})

= ln (2^{2} \cdot \frac{1}{60})

\frac{1}{60} \cdot 2^{2} = \frac{1}{15}

= ln (\frac{1}{15})

Apply log rule:

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

= - ln (15)

ln (\frac{s ^{2}}{( s - 9 ) ^{2}})

ln (\frac{x ^{2}}{e ^{3}})

ln (\frac{2.9}{12})

\frac{ln ( 3.1 ) - ln ( 3 )}{3.1 - 3}

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

What is simplify-2ln(6)-ln(5)+ln(3)+2ln(2) ?
The solution to simplify-2ln(6)-ln(5)+ln(3)+2ln(2) is -ln(15)