What is 0.23*ln(0.23)+5.55ln(0.76) ?

The solution to 0.23*ln(0.23)+5.55ln(0.76) is ln(0.15549…)

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simplify 0.23*ln(0.23)+5.55ln(0.76)

simplify

0.23 \cdot ln (0.23) + 5.55 ln (0.76)

ln (0.15549 \dots)

Decimal Notation

- 1.86114 \dots

Solution steps

0.23 ln (0.23) + 5.55 ln (0.76)

Apply log rule:

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

0.23 ln (0.23) = ln (0.2 3^{0.23})

= ln (0.2 3^{0.23}) + 5.55 ln (0.76)

Apply log rule:

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

5.55 ln (0.76) = ln (0.7 6^{5.55})

= ln (0.2 3^{0.23}) + ln (0.7 6^{5.55})

Apply log rule:

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

ln (0.2 3^{0.23}) + ln (0.7 6^{5.55}) = ln (0.7 6^{5.55} \cdot 0.2 3^{0.23})

= ln (0.7 6^{5.55} \cdot 0.2 3^{0.23})

0.2 3^{0.23} \cdot 0.7 6^{5.55} = 0.15549 \dots

= ln (0.15549 \dots)

ln (\frac{x - 1}{x + 3})

ln (2) - ln (2 + 1)

ln (4.4 \cdot 1 0^{15})

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

4.57 + lo g_{10} (\frac{0.049}{0.21})

What is 0.23*ln(0.23)+5.55ln(0.76) ?
The solution to 0.23*ln(0.23)+5.55ln(0.76) is ln(0.15549…)