What is 0.026*ln((10^{17})/(1.4*10^{10)}) ?

The solution to 0.026*ln((10^{17})/(1.4*10^{10)}) is 0.026(17ln(10)-ln(1.4*10^{10}))

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simplify 0.026ln((10^{17})/(1.410^{10)})

simplify

0.026 \cdot ln (\frac{1 0 ^{17}}{1.4 \cdot 1 0 ^{10}})

0.026 (17 ln (10) - ln (1.4 \cdot 1 0^{10}))

Decimal Notation

0.41032 \dots

Solution steps

0.026 ln (\frac{1 0 ^{17}}{1.4 \cdot 1 0 ^{10}})

Apply log rule:

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

ln (\frac{1 0 ^{17}}{1.4 \cdot 1 0 ^{10}}) = ln (1 0^{17}) - ln (1.4 \cdot 1 0^{10})

= 0.026 (ln (1 0^{17}) - ln (1 0^{10} \cdot 1.4))

Apply log rule:

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

ln (1 0^{17}) = 17 ln (10)

= 0.026 (17 ln (10) - ln (1.4 \cdot 1 0^{10}))

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What is 0.026*ln((10^{17})/(1.4*10^{10)}) ?
The solution to 0.026*ln((10^{17})/(1.4*10^{10)}) is 0.026(17ln(10)-ln(1.4*10^{10}))