What is ln((3.64)/(23))+3/23 ln(23) ?

The solution to ln((3.64)/(23))+3/23 ln(23) is ln(0.23822…)

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simplify ln((3.64)/(23))+3/23 ln(23)

simplify

ln (\frac{3.64}{23}) + \frac{3}{23} ln (23)

ln (0.23822 \dots)

Decimal Notation

- 1.43453 \dots

Solution steps

ln (\frac{3.64}{23}) + \frac{3}{23} ln (23)

Apply log rule:

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

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

= ln (\frac{3.64}{23}) + ln (2 3^{\frac{3}{23}})

Apply log rule:

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

ln (\frac{3.64}{23}) + ln (2 3^{\frac{3}{23}}) = ln (2 3^{\frac{3}{23}} \cdot \frac{3.64}{23})

= ln (2 3^{\frac{3}{23}} \cdot \frac{3.64}{23})

\frac{3.64}{23} \cdot 2 3^{\frac{3}{23}} = 0.23822 \dots

= ln (0.23822 \dots)

\frac{1}{3} ln (\frac{17}{3} + 35)

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

ln (\frac{2.5}{3})

lo g_{4} (\frac{x}{16})

ln (x^{4}) + ln (\frac{1}{x})

What is ln((3.64)/(23))+3/23 ln(23) ?
The solution to ln((3.64)/(23))+3/23 ln(23) is ln(0.23822…)