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

The solution to 2ln(3)+2ln(2) is 2ln(6)

Popular >

simplify 2ln(3)+2ln(2)

simplify

2 ln (3) + 2 ln (2)

2 ln (6)

Decimal Notation

3.58351 \dots

Solution steps

2 ln (3) + 2 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} \cdot 2^{2} = 36

= ln (36)

Rewrite

36

in power-base form:

36 = 6^{2}

= ln (6^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (6)

\frac{3}{2} \cdot ln^{3} (3)

- lo g_{10} (1.58 \cdot 1 0^{- 3})

\frac{3}{5} ln ∣ 4 - 1 ∣ + \frac{2}{5} ln ∣ 4 + 4 ∣

4 ln (1) - 3 ln (2) - 4 ln (\frac{1}{2}) - 3 ln (\frac{1}{2} + 1)

ln (\frac{25}{36})