What is ln(sqrt(e))+4ln(\sqrt[3]{e})-2ln(1/e) ?

The solution to ln(sqrt(e))+4ln(\sqrt[3]{e})-2ln(1/e) is ln(sqrt(e)e^{4/3})+2

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simplify ln(sqrt(e))+4ln(\sqrt[3]{e})-2ln(1/e)

simplify

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

Decimal Notation

3.83333 \dots

Solution steps

Apply log rule:

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

Apply log rule:

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

= ln (e e^{\frac{4}{3}}) - 2 ln (\frac{1}{e})

2 ln (\frac{1}{e}) = - 2

= ln (e e^{\frac{4}{3}}) - (- 2)

Apply rule

- (- a) = a

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

3 lo g_{10} (x) + 2 lo g_{10} (y) - lo g_{10} (z)

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

lo g_{g} (\frac{s t ^{6}}{r ^{7}})

lo g_{10} (8) - lo g_{10} (4)

lo g_{10} (y z^{7})

What is ln(sqrt(e))+4ln(\sqrt[3]{e})-2ln(1/e) ?
The solution to ln(sqrt(e))+4ln(\sqrt[3]{e})-2ln(1/e) is ln(sqrt(e)e^{4/3})+2