What is 25*10^{-3}*ln((10^{-2})/(10^{-9)}) ?

The solution to 25*10^{-3}*ln((10^{-2})/(10^{-9)}) is (7ln(10))/(40)

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simplify 2510^{-3}ln((10^{-2})/(10^{-9)})

simplify

25 \cdot 1 0^{- 3} \cdot ln (\frac{1 0 ^{- 2}}{1 0 ^{- 9}})

\frac{7 ln ( 10 )}{40}

Decimal Notation

0.40295 \dots

Solution steps

25 \cdot 1 0^{- 3} ln (\frac{1 0 ^{- 2}}{1 0 ^{- 9}})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 25 \cdot \frac{1}{1 0 ^{3}} ln (\frac{1 0 ^{- 2}}{1 0 ^{- 9}})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 25 ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{1 0 ^{3}}

Multiply the numbers:

1 \cdot 25 = 25

= \frac{25 ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{1 0 ^{3}}

Factor

25 : 5^{2}

Factor

1 0^{3} : 2^{3} \cdot 5^{3}

= \frac{5 ^{2} ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{2 ^{3} \cdot 5 ^{3}}

Cancel

\frac{5 ^{2} ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{2 ^{3} \cdot 5 ^{3}} : \frac{ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{2 ^{3} \cdot 5}

= \frac{ln ( \frac{1 0 ^{- 2}}{1 0 ^{- 9}} )}{2 ^{3} \cdot 5}

\frac{1 0 ^{- 2}}{1 0 ^{- 9}} = 1 0^{7}

= \frac{ln ( 1 0 ^{7} )}{2 ^{3} \cdot 5}

Simplify

ln (1 0^{7}) : 7 ln (10)

= \frac{7 ln ( 10 )}{2 ^{3} \cdot 5}

2^{3} \cdot 5 = 40

= \frac{7 ln ( 10 )}{40}

x + 1 \times x - 4

e^{- s t} e^{t - 1}

\frac{( x + 7 ) ( x + 2 )}{1 - x}

What is 25*10^{-3}*ln((10^{-2})/(10^{-9)}) ?
The solution to 25*10^{-3}*ln((10^{-2})/(10^{-9)}) is (7ln(10))/(40)