What is (4186)ln(0.77090493)-8.314ln(0.1) ?

The solution to (4186)ln(0.77090493)-8.314ln(0.1) is 4186ln(0.77090493^{4186}*206062991.32699…)

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simplify (4186)ln(0.77090493)-8.314ln(0.1)

simplify

(4186) ln (0.77090493) - 8.314 ln (0.1)

4186 ln (0.7709049 3^{4186} \cdot 206062991.32699 \dots)

Solution steps

(4186) ln (0.77090493) - 8.314 ln (0.1)

Apply log rule:

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

8.314 ln (0.1) = ln (0. 1^{8.314})

= (4186) ln (0.77090493) - ln (0. 1^{8.314})

Apply log rule:

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

ln (0.77090493) - ln (0. 1^{8.314}) = ln (\frac{0.77090493}{0. 1 ^{8.314}})

= 4186 ln (\frac{0.77090493}{0. 1 ^{8.314}})

Simplify

\frac{0.7709049 3 ^{(4186)}}{0. 1 ^{8.314}} : 0.7709049 3^{4186} \cdot 206062991.32699 \dots

= 4186 ln (0.7709049 3^{4186} \cdot 206062991.32699 \dots)

ln (y^{x} e^{- y})

lo g_{2} (0.05) + lo g_{2} (0.9)

1 + \frac{1}{50000 ln ( 5 )}

ln (\frac{1 0 ^{2}}{8 ^{2}})

2.06 \cdot ln (\frac{2}{1})

What is (4186)ln(0.77090493)-8.314ln(0.1) ?
The solution to (4186)ln(0.77090493)-8.314ln(0.1) is 4186ln(0.77090493^{4186}*206062991.32699…)