What is 2ln(2)+1.5ln(3)-0.5 ?

The solution to 2ln(2)+1.5ln(3)-0.5 is ln(20.78460…)-0.5

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simplify 2ln(2)+1.5ln(3)-0.5

simplify

2 ln (2) + 1.5 ln (3) - 0.5

ln (20.78460 \dots) - 0.5

Decimal Notation

2.53421 \dots

Solution steps

2 ln (2) + 1.5 ln (3) - 0.5

Apply log rule:

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

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

= ln (2^{2}) + 1.5 ln (3) - 0.5

Apply log rule:

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

1.5 ln (3) = ln (3^{1.5})

= ln (2^{2}) + ln (3^{1.5}) - 0.5

Apply log rule:

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

ln (2^{2}) + ln (3^{1.5}) = ln (2^{2} \cdot 3^{1.5})

= ln (2^{2} \cdot 3^{1.5}) - 0.5

2^{2} \cdot 3^{1.5} = 20.78460 \dots

= ln (20.78460 \dots) - 0.5

ln (\frac{e ^{3}}{1 - e ^{3}})

ln (\frac{t}{5})

ln (19) - ln (3)

lo g_{3} ((5 x)^{3})

ln (\frac{5 + 0.5}{5})

What is 2ln(2)+1.5ln(3)-0.5 ?
The solution to 2ln(2)+1.5ln(3)-0.5 is ln(20.78460…)-0.5