What is (2ln(3)+2ln(5))/4 ?

The solution to (2ln(3)+2ln(5))/4 is (ln(15))/2

Popular >

simplify (2ln(3)+2ln(5))/4

simplify

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

\frac{ln ( 15 )}{2}

Decimal Notation

1.35402 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 ln (5) = ln (5^{2})

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

Apply log rule:

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

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

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

3^{2} \cdot 5^{2} = 225

= \frac{ln ( 225 )}{4}

Simplify

ln (225) : 2 ln (15)

= \frac{2 ln ( 15 )}{4}

Cancel the common factor:

2

= \frac{ln ( 15 )}{2}

lo g_{6} (36 x^{3})

lo g_{10} (x^{\frac{1}{2}} y^{\frac{1}{3}})

- lo g_{10} (6.2 \cdot 1 0^{- 8})

ln (a e^{b x})

\frac{1}{3} ln \frac{3 ( e ^{x^{3}} ) ^{3}}{x ^{6}}