What is ln(94.72)0.42+ln(138.96)0.58 ?

The solution to ln(94.72)0.42+ln(138.96)0.58 is ln(118.29914…)

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simplify ln(94.72)0.42+ln(138.96)0.58

simplify

ln (94.72) 0.42 + ln (138.96) 0.58

ln (118.29914 \dots)

Decimal Notation

4.77321 \dots

Solution steps

ln (94.72) \cdot 0.42 + ln (138.96) \cdot 0.58

Apply log rule:

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

0.42 ln (94.72) = ln (94.7 2^{0.42})

= ln (94.7 2^{0.42}) + 0.58 ln (138.96)

Apply log rule:

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

0.58 ln (138.96) = ln (138.9 6^{0.58})

= ln (94.7 2^{0.42}) + ln (138.9 6^{0.58})

Apply log rule:

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

ln (94.7 2^{0.42}) + ln (138.9 6^{0.58}) = ln (94.7 2^{0.42} \cdot 138.9 6^{0.58})

= ln (94.7 2^{0.42} \cdot 138.9 6^{0.58})

94.7 2^{0.42} \cdot 138.9 6^{0.58} = 118.29914 \dots

= ln (118.29914 \dots)

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

ln (\frac{x}{y} - 1) - ln (y)

ln (6 \cdot 1 0^{- 6})

- lo g_{10} (3.5 \cdot 1 0^{- 9})

lo g_{10} (40) - lo g_{10} (2.5)

What is ln(94.72)0.42+ln(138.96)0.58 ?
The solution to ln(94.72)0.42+ln(138.96)0.58 is ln(118.29914…)