What is simplify-5ln(2)+3ln(3) ?

The solution to simplify-5ln(2)+3ln(3) is ln(27/32)

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simplify-5ln(2)+3ln(3)

simplify

- 5 ln (2) + 3 ln (3)

ln (\frac{27}{32})

Decimal Notation

- 0.16989 \dots

Solution steps

- 5 ln (2) + 3 ln (3)

Apply log rule:

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

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

= - ln (2^{5}) + 3 ln (3)

Apply log rule:

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

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

= - ln (2^{5}) + ln (3^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

\frac{3 ^{3}}{2 ^{5}} = \frac{27}{32}

= ln (\frac{27}{32})

2^{\frac{3 l o g _{2} ( 5 )}{2}} - 3

lo g_{2} (6) - lo g_{2} (15) lo g_{2} (20)

2 ln (x^{0.5} y^{0.5})

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

1 + \frac{1}{2} lo g_{10} (p + 4) - lo g_{10} (x)

What is simplify-5ln(2)+3ln(3) ?
The solution to simplify-5ln(2)+3ln(3) is ln(27/32)