What is simplify-12ln(3+5)+12ln(3+2) ?

The solution to simplify-12ln(3+5)+12ln(3+2) is ln((244140625)/(8^{12)})

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simplify-12ln(3+5)+12ln(3+2)

simplify

- 12 ln (3 + 5) + 12 ln (3 + 2)

ln (\frac{244140625}{8 ^{12}})

Decimal Notation

- 5.64004 \dots

Solution steps

- 12 ln (3 + 5) + 12 ln (3 + 2)

Apply log rule:

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

12 ln (3 + 5) = ln ((3 + 5)^{12})

= - ln ((3 + 5)^{12}) + 12 ln (3 + 2)

Apply log rule:

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

12 ln (3 + 2) = ln ((3 + 2)^{12})

= - ln ((3 + 5)^{12}) + ln ((3 + 2)^{12})

Apply log rule:

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

ln ((3 + 2)^{12}) - ln ((3 + 5)^{12}) = ln (\frac{( 3 + 2 ) ^{12}}{( 3 + 5 ) ^{12}})

= ln (\frac{( 3 + 2 ) ^{12}}{( 3 + 5 ) ^{12}})

\frac{( 3 + 2 ) ^{12}}{( 3 + 5 ) ^{12}} = \frac{244140625}{8 ^{12}}

= ln (\frac{244140625}{8 ^{12}})

lo g_{e} (2 e^{3 x})

- 2 ln (y) - ln (x)

4 ln (x - 4) + 5 ln (x - 5) + c

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

- ln (\frac{2.8}{5}) \cdot 52.41

What is simplify-12ln(3+5)+12ln(3+2) ?
The solution to simplify-12ln(3+5)+12ln(3+2) is ln((244140625)/(8^{12)})