What is 0.7ln((0.7m)/p)+0.3ln((0.3m)/b) ?

The solution to 0.7ln((0.7m)/p)+0.3ln((0.3m)/b) is ln(((0.7m)/p)^{0.7}((0.3m)/b)^{0.3})

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simplify 0.7ln((0.7m)/p)+0.3ln((0.3m)/b)

simplify

0.7 ln (\frac{0.7 m}{p}) + 0.3 ln (\frac{0.3 m}{b})

ln ((\frac{0.7 m}{p})^{0.7} (\frac{0.3 m}{b})^{0.3})

Solution steps

0.7 ln (\frac{0.7 m}{p}) + 0.3 ln (\frac{0.3 m}{b})

Apply log rule:

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

0.7 ln (\frac{0.7 m}{p}) = ln ((\frac{0.7 m}{p})^{0.7})

= ln ((\frac{0.7 m}{p})^{0.7}) + 0.3 ln (\frac{0.3 m}{b})

Apply log rule:

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

0.3 ln (\frac{0.3 m}{b}) = ln ((\frac{0.3 m}{b})^{0.3})

= ln ((\frac{0.7 m}{p})^{0.7}) + ln ((\frac{0.3 m}{b})^{0.3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((\frac{0.7 m}{p})^{0.7}) + ln ((\frac{0.3 m}{b})^{0.3}) = ln ((\frac{0.7 m}{p})^{0.7} (\frac{0.3 m}{b})^{0.3})

= ln ((\frac{0.7 m}{p})^{0.7} (\frac{0.3 m}{b})^{0.3})

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- lo g_{10} (4 (1 0^{- 5}))

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ln (60) + ln (10)

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What is 0.7ln((0.7m)/p)+0.3ln((0.3m)/b) ?
The solution to 0.7ln((0.7m)/p)+0.3ln((0.3m)/b) is ln(((0.7m)/p)^{0.7}((0.3m)/b)^{0.3})