What is ln(1/3)-sqrt(e^{-(3)^3)} ?

The solution to ln(1/3)-sqrt(e^{-(3)^3)} is -ln(3)-sqrt(1/(e^{27))}

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simplify ln(1/3)-sqrt(e^{-(3)^3)}

simplify

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

- ln (3) - \frac{1}{e ^{27}}

Decimal Notation

- 1.09861 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{1}{3}) = ln (1) - ln (3)

= ln (1) - ln (3) - e^{- 3^{3}}

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (3) - e^{- 3^{3}}

0 - ln (3) - e^{- 3^{3}} = - ln (3) - e^{- 3^{3}}

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

e^{- 3^{3}} = \frac{1}{e ^{27}}

= - ln (3) - \frac{1}{e ^{27}}

lo g_{1.8} (\frac{3.57}{3.92}) + 50.65 - 51.6

ln (\frac{1}{2}) - 2 + 3 ln (2)

ln (9) + ln (2)

2 [(ln (x + 3) + ln (x) - ln (x^{2} - 1))]

ln (\frac{x ^{2}}{y ^{3} z ^{4}})

What is ln(1/3)-sqrt(e^{-(3)^3)} ?
The solution to ln(1/3)-sqrt(e^{-(3)^3)} is -ln(3)-sqrt(1/(e^{27))}