What is 0.025ln((2*10^{18}*10^{20})/(10^{20)}) ?

The solution to 0.025ln((2*10^{18}*10^{20})/(10^{20)}) is 0.025(ln(10^{38}*2)-20ln(10))

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simplify 0.025ln((210^{18}10^{20})/(10^{20)})

simplify

0.025 ln (\frac{2 \cdot 1 0 ^{18} \cdot 1 0 ^{20}}{1 0 ^{20}})

0.025 (ln (1 0^{38} \cdot 2) - 20 ln (10))

Decimal Notation

1.05349 \dots

Solution steps

0.025 ln (\frac{2 \cdot 1 0 ^{18} \cdot 1 0 ^{20}}{1 0 ^{20}})

Apply log rule:

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

ln (\frac{2 \cdot 1 0 ^{18} \cdot 1 0 ^{20}}{1 0 ^{20}}) = ln (2 \cdot 1 0^{18} \cdot 1 0^{20}) - ln (1 0^{20})

= 0.025 (ln (1 0^{20} \cdot 1 0^{18} \cdot 2) - ln (1 0^{20}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{20}) = 20 ln (10)

= 0.025 (ln (2 \cdot 1 0^{18} \cdot 1 0^{20}) - 20 ln (10))

Simplify

2 \cdot 1 0^{18} \cdot 1 0^{20} : 1 0^{38} \cdot 2

= 0.025 (ln (1 0^{38} \cdot 2) - 20 ln (10))

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

ln (ln (x) + ln (y))

ln (0.03 t \cdot e^{- \frac{6}{100} t})

21 lo g_{10} (x) + lo g_{10} (5)

- lo g_{10} (3 \cdot 1 0^{- 17})

What is 0.025ln((2*10^{18}*10^{20})/(10^{20)}) ?
The solution to 0.025ln((2*10^{18}*10^{20})/(10^{20)}) is 0.025(ln(10^{38}*2)-20ln(10))