Respuesta :
Answer:
1) 1.7917
2) 0.4055
3) 4.3944
4) 0.5493
Step-by-step explanation:
We are given the following:
[tex]\ln 2 \approx 0.6931\\\ln 3 \approx 1.0986[/tex]
We have to evaluate the following:
1) In 6
Logarithmic property:
[tex]\ln (a\times b) = \ln a + \ln b[/tex]
[tex]\ln 6 = \ln (2\times 3)\\= \ln 2 +\ln 3\\= 0.6931 + 1.0986\\=1.7917[/tex]
2) [tex]\ln (\frac{3}{2})[/tex]
Logarithmic property:
[tex]\ln \dfrac{a}{b} = \ln a - \ln b[/tex]
[tex]\ln \dfrac{3}{2} = \ln 3 - \ln 2 \\\\= 1.0986 - 0.6931\\=0.4055[/tex]
3) In 81
Logarithmic property:
[tex]\ln(a^x) = x\ln a[/tex]
[tex]\ln 81 = \ln(3^4)\\=4\ln 3\\=4\times 1.0986\\=4.3944[/tex]
4) [tex]\ln (3)^{\frac{1}{2}}[/tex]
Logarithmic property:
[tex]\ln(a^x) = x\ln a[/tex]
[tex]\ln (3)^{\frac{1}{2}}\\\\=\dfrac{1}{2}\ln 3\\\\=\dfrac{1}{2}\times 1.0986\\\\=0.5493[/tex]
