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(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 (24)

Decimal Notation

- 3.17805 \dots

Solution steps

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

Rewrite

- ln (6) - ln (5)

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

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

Apply log rule:

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

ln (6) + ln (5) = ln (6 \cdot 5)

= - ln (6 \cdot 5) + ln (5) - 2 ln (2)

Multiply the numbers:

6 \cdot 5 = 30

= - ln (30) + 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 (30) = ln (\frac{5}{30})

= ln (\frac{5}{30}) - 2 ln (2)

Cancel the common factor:

5

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

Apply log rule:

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

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

= ln (\frac{\frac{1}{6}}{2 ^{2}})

\frac{\frac{1}{6}}{2 ^{2}} = \frac{1}{24}

= ln (\frac{1}{24})

Apply log rule:

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

= - ln (24)

\frac{0.0030597}{0.5 \cdot \frac{1}{60}} ln (\frac{0.008}{0.04})

\frac{1}{0. 1 ^{2}} ln (\frac{1}{0.1})

ln (\frac{( x ) ( x ^{2} + 1 ) ^{2}}{2 x ^{3} - 1})

lo g_{4} (\frac{( a ^{2} \cdot b ^{3} )}{c \cdot d})

lo g_{10} (2) - lo g_{10} (3 i)

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(24)