What is 4ln(2)+2ln(3) ?

The solution to 4ln(2)+2ln(3) is 2ln(12)

Popular >

simplify 4ln(2)+2ln(3)

simplify

4 ln (2) + 2 ln (3)

2 ln (12)

Decimal Notation

4.96981 \dots

Solution steps

4 ln (2) + 2 ln (3)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (2^{4}) + 2 ln (3)

Apply log rule:

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

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

= ln (2^{4}) + ln (3^{2})

Apply log rule:

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

ln (2^{4}) + ln (3^{2}) = ln (2^{4} \cdot 3^{2})

= ln (2^{4} \cdot 3^{2})

2^{4} \cdot 3^{2} = 144

= ln (144)

Rewrite

144

in power-base form:

144 = 1 2^{2}

= ln (1 2^{2})

Apply log rule:

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

ln (1 2^{2}) = 2 ln (12)

= 2 ln (12)

ln (2 p) - 1

ln (\frac{( 2 ^{2} )}{3 ^{4} 5 ^{3}})

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

ln (0.5 t e^{- 0.5 t})

6 lo g_{e} (x) + 4 lo g_{e} (y)