What is simplify-3ln(2)-ln(3) ?

The solution to simplify-3ln(2)-ln(3) is -ln(24)

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simplify-3ln(2)-ln(3)

simplify

- 3 ln (2) - ln (3)

- ln (24)

Decimal Notation

- 3.17805 \dots

Solution steps

- 3 ln (2) - ln (3)

Apply log rule:

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

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

= - ln (2^{3}) - ln (3)

Rewrite

- ln (2^{3}) - ln (3)

- (ln (2^{3}) + ln (3))

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

Apply log rule:

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

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

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

2^{3} \cdot 3 = 24

= - ln (24)

- lo g_{10} (5.7 \cdot 1 0^{- 4})

lo g_{3} (11 p^{3})

5 ln (\frac{3}{4}) + \frac{5 - 3 ln ( \frac{81}{64} )}{2}

ln (10 x + 3) + ln (x + 3)

ln ((\frac{1}{2} + \frac{x}{4})^{a} \cdot (\frac{1}{4} - \frac{x}{4})^{b + c} \cdot (\frac{x}{4})^{d})

What is simplify-3ln(2)-ln(3) ?
The solution to simplify-3ln(2)-ln(3) is -ln(24)