What is ln(1/5)-sqrt(e^{(-5^3))} ?

The solution to ln(1/5)-sqrt(e^{(-5^3))} is -ln(5)-sqrt(1/(e^{125))}

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simplify ln(1/5)-sqrt(e^{(-5^3))}

simplify

ln (\frac{1}{5}) - e^{(- 5^{3})}

- ln (5) - \frac{1}{e ^{125}}

Decimal Notation

- 1.60943 \dots

Solution steps

ln (\frac{1}{5}) - e^{(- 5^{3})}

Apply log rule:

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

ln (\frac{1}{5}) = ln (1) - ln (5)

= ln (1) - ln (5) - e^{- 5^{3}}

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (5) - e^{- 5^{3}}

0 - ln (5) - e^{- 5^{3}} = - ln (5) - e^{- 5^{3}}

= - ln (5) - e^{- 5^{3}}

e^{- 5^{3}} = \frac{1}{e ^{125}}

= - ln (5) - \frac{1}{e ^{125}}

8 \cdot ln (\frac{8}{9.1161})

lo g_{10} (\frac{1}{2.5 \cdot 1 0 ^{- 9}})

- 2 ln (\frac{3 e ^{- n^{3} + n x}}{x})

\frac{1}{3} ln ((x + 2)^{3}) + \frac{1}{2} ln (\frac{x}{( x ^{2} + 3 x + 2 ) ^{2}})

- lo g_{10} (1.2 \cdot 1 0^{- 12})

What is ln(1/5)-sqrt(e^{(-5^3))} ?
The solution to ln(1/5)-sqrt(e^{(-5^3))} is -ln(5)-sqrt(1/(e^{125))}