What is (2ln(3)+3ln(2))-(2ln(2)+3ln(1)) ?

The solution to (2ln(3)+3ln(2))-(2ln(2)+3ln(1)) is ln(72)-2ln(2)

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

simplify

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

ln (72) - 2 ln (2)

Decimal Notation

2.89037 \dots

Solution steps

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

Apply log rule:

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

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

= (3 ln (2) + ln (3^{2})) - (2 ln (2) + 3 ln (1))

Apply log rule:

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

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

= (ln (3^{2}) + ln (2^{3})) - (2 ln (2) + 3 ln (1))

Apply log rule:

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

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

= ln (2^{3} \cdot 3^{2}) - (2 ln (2) + 3 ln (1))

3^{2} \cdot 2^{3} = 72

= ln (72) - (2 ln (2) + 3 ln (1))

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

= ln (72) - 2 ln (2)

lo g_{4} (7 \cdot 9 \cdot 3)

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

\frac{1}{7} (lo g_{2} (x) + lo g_{2} (y))

lo g_{3} (5) - lo g_{3} (7)

lo g_{5} (25 x) + lo g_{5} (w)

What is (2ln(3)+3ln(2))-(2ln(2)+3ln(1)) ?
The solution to (2ln(3)+3ln(2))-(2ln(2)+3ln(1)) is ln(72)-2ln(2)