What is ln(3/23)+(2/23)ln(23) ?

The solution to ln(3/23)+(2/23)ln(23) is ln((3*23^{2/23})/(23))

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simplify ln(3/23)+(2/23)ln(23)

simplify

ln (\frac{3}{23}) + (\frac{2}{23}) ln (23)

ln (\frac{3 \cdot 2 3 ^{\frac{2}{23}}}{23})

Decimal Notation

- 1.76423 \dots

Solution steps

ln (\frac{3}{23}) + (\frac{2}{23}) ln (23)

Apply log rule:

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

(\frac{2}{23}) ln (23) = ln (2 3^{(\frac{2}{23})})

= ln (\frac{3}{23}) + ln (2 3^{(\frac{2}{23})})

Apply log rule:

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

ln (\frac{3}{23}) + ln (2 3^{(\frac{2}{23})}) = ln (2 3^{\frac{2}{23}} \cdot \frac{3}{23})

= ln (2 3^{\frac{2}{23}} \cdot \frac{3}{23})

\frac{3}{23} \cdot 2 3^{(\frac{2}{23})} = \frac{3 \cdot 2 3 ^{\frac{2}{23}}}{23}

= ln (\frac{3 \cdot 2 3 ^{\frac{2}{23}}}{23})

ln (178) - ln (713)

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4 lo g_{10} (r) - lo g_{10} (c x)

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What is ln(3/23)+(2/23)ln(23) ?
The solution to ln(3/23)+(2/23)ln(23) is ln((3*23^{2/23})/(23))