What is 14.307ln((396.5)/(303))-4.124ln(3) ?

The solution to 14.307ln((396.5)/(303))-4.124ln(3) is ln(0.50514…)

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simplify 14.307ln((396.5)/(303))-4.124ln(3)

simplify

14.307 ln (\frac{396.5}{303}) - 4.124 ln (3)

ln (0.50514 \dots)

Decimal Notation

- 0.68290 \dots

Solution steps

14.307 ln (\frac{396.5}{303}) - 4.124 ln (3)

Apply log rule:

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

14.307 ln (\frac{396.5}{303}) = ln ((\frac{396.5}{303})^{14.307})

= ln ((\frac{396.5}{303})^{14.307}) - 4.124 ln (3)

Apply log rule:

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

4.124 ln (3) = ln (3^{4.124})

= ln ((\frac{396.5}{303})^{14.307}) - ln (3^{4.124})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((\frac{396.5}{303})^{14.307}) - ln (3^{4.124}) = ln (\frac{( \frac{396.5}{303} ) ^{14.307}}{3 ^{4.124}})

= ln (\frac{( \frac{396.5}{303} ) ^{14.307}}{3 ^{4.124}})

\frac{( \frac{396.5}{303} ) ^{14.307}}{3 ^{4.124}} = 0.50514 \dots

= ln (0.50514 \dots)

ln (\frac{58387}{88})

- \frac{1}{2} ln ∣ x ∣ + ln ∣ y ∣

- lo g_{10} (4.9 \cdot 1 0^{- 10} \cdot 0.1)

\frac{1}{75} ln (\frac{1}{12})

lo g_{10} (x^{2} y^{2} x y)

What is 14.307ln((396.5)/(303))-4.124ln(3) ?
The solution to 14.307ln((396.5)/(303))-4.124ln(3) is ln(0.50514…)