What is 1.005*ln(500/1400)-0.287ln(500/2000) ?

The solution to 1.005*ln(500/1400)-0.287ln(500/2000) is ln(0.52892…)

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simplify 1.005*ln(500/1400)-0.287ln(500/2000)

simplify

1.005 \cdot ln (\frac{500}{1400}) - 0.287 ln (\frac{500}{2000})

ln (0.52892 \dots)

Decimal Notation

- 0.63690 \dots

Solution steps

1.005 ln (\frac{500}{1400}) - 0.287 ln (\frac{500}{2000})

Apply log rule:

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

1.005 ln (\frac{500}{1400}) = ln ((\frac{500}{1400})^{1.005})

= ln ((\frac{500}{1400})^{1.005}) - 0.287 ln (\frac{500}{2000})

Apply log rule:

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

0.287 ln (\frac{500}{2000}) = ln ((\frac{500}{2000})^{0.287})

= ln ((\frac{500}{1400})^{1.005}) - ln ((\frac{500}{2000})^{0.287})

Apply log rule:

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

ln ((\frac{500}{1400})^{1.005}) - ln ((\frac{500}{2000})^{0.287}) = ln (\frac{( \frac{500}{1400} ) ^{1.005}}{( \frac{500}{2000} ) ^{0.287}})

= ln (\frac{( \frac{500}{1400} ) ^{1.005}}{( \frac{500}{2000} ) ^{0.287}})

\frac{( \frac{500}{1400} ) ^{1.005}}{( \frac{500}{2000} ) ^{0.287}} = 0.52892 \dots

= ln (0.52892 \dots)

3.34 + lo g_{10} (\frac{0.00546}{0.00671})

ln (\frac{1}{1 - x ^{2}})

- lo g_{10} (2.07 (1 0^{- 6}))

ln (a r (a x)^{r - 1} e^{- (a x)^{r}})

3 ln (2) + 4 ln (5)

What is 1.005*ln(500/1400)-0.287ln(500/2000) ?
The solution to 1.005*ln(500/1400)-0.287ln(500/2000) is ln(0.52892…)