What is 0.3*ln(600)+0.7*ln(54 6/11) ?

The solution to 0.3*ln(600)+0.7*ln(54 6/11) is ln(111.98925…)

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simplify 0.3ln(600)+0.7ln(54 6/11)

simplify

0.3 \cdot ln (600) + 0.7 \cdot ln (54 \frac{6}{11})

ln (111.98925 \dots)

Decimal Notation

4.71840 \dots

Solution steps

0.3 \cdot ln (600) + 0.7 \cdot ln (54 \frac{6}{11})

Convert mixed numbers to improper fractions:

54 \frac{6}{11} = \frac{600}{11}

= 0.3 \cdot ln (600) + 0.7 \cdot ln (\frac{600}{11})

Apply log rule:

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

0.3 ln (600) = ln (60 0^{0.3})

= ln (60 0^{0.3}) + 0.7 ln (\frac{600}{11})

Apply log rule:

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

0.7 ln (\frac{600}{11}) = ln ((\frac{600}{11})^{0.7})

= ln (60 0^{0.3}) + ln ((\frac{600}{11})^{0.7})

Apply log rule:

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

ln (60 0^{0.3}) + ln ((\frac{600}{11})^{0.7}) = ln (60 0^{0.3} (\frac{600}{11})^{0.7})

= ln (60 0^{0.3} (\frac{600}{11})^{0.7})

60 0^{0.3} (\frac{600}{11})^{0.7} = 111.98925 \dots

= ln (111.98925 \dots)

ln (\frac{11}{2}) + 1 + \frac{1}{( \frac{11}{2} ) ^{2}}

ln ((t + 1) (\frac{4 t ^{3}}{3}) (2 t^{2}) (C))

ln (3 \cdot 1 0^{- 3})

ln (- e^{- 4 x}) + ln (e^{4 x})

15 ln (15)^{2} + 7 - 15 ln (0)^{2} + 7

What is 0.3*ln(600)+0.7*ln(54 6/11) ?
The solution to 0.3*ln(600)+0.7*ln(54 6/11) is ln(111.98925…)