What is 0.3*ln(600)+0.7*ln(28 4/7) ?

The solution to 0.3*ln(600)+0.7*ln(28 4/7) is ln(71.21930…)

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simplify 0.3ln(600)+0.7ln(28 4/7)

simplify

0.3 \cdot ln (600) + 0.7 \cdot ln (28 \frac{4}{7})

ln (71.21930 \dots)

Decimal Notation

4.26576 \dots

Solution steps

0.3 \cdot ln (600) + 0.7 \cdot ln (28 \frac{4}{7})

Convert mixed numbers to improper fractions:

28 \frac{4}{7} = \frac{200}{7}

= 0.3 \cdot ln (600) + 0.7 \cdot ln (\frac{200}{7})

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{200}{7})

Apply log rule:

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

0.7 ln (\frac{200}{7}) = ln ((\frac{200}{7})^{0.7})

= ln (60 0^{0.3}) + ln ((\frac{200}{7})^{0.7})

Apply log rule:

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

ln (60 0^{0.3}) + ln ((\frac{200}{7})^{0.7}) = ln (60 0^{0.3} (\frac{200}{7})^{0.7})

= ln (60 0^{0.3} (\frac{200}{7})^{0.7})

60 0^{0.3} (\frac{200}{7})^{0.7} = 71.21930 \dots

= ln (71.21930 \dots)

ln (r) - ln (x)

2 ln (y) + \frac{9}{5} ln (y + 2) + \frac{1}{5} ln (y - 3)

ln (\frac{80}{9996.6})

lo g_{10} (\frac{4 x ^{6}}{- 1})

2 lo g_{8} (z) - \frac{1}{2} lo g_{8} (w) + 4 lo g_{8} (x)

What is 0.3*ln(600)+0.7*ln(28 4/7) ?
The solution to 0.3*ln(600)+0.7*ln(28 4/7) is ln(71.21930…)