What is (0.287)ln(500/200)-(1.05)ln(680/980) ?

The solution to (0.287)ln(500/200)-(1.05)ln(680/980) is ln(1.90924…)

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simplify (0.287)ln(500/200)-(1.05)ln(680/980)

simplify

(0.287) ln (\frac{500}{200}) - (1.05) ln (\frac{680}{980})

ln (1.90924 \dots)

Decimal Notation

0.64670 \dots

Solution steps

(0.287) ln (\frac{500}{200}) - (1.05) ln (\frac{680}{980})

Apply log rule:

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

(0.287) ln (\frac{500}{200}) = ln ((\frac{500}{200})^{(0.287)})

= ln ((\frac{500}{200})^{(0.287)}) - (1.05) ln (\frac{680}{980})

Apply log rule:

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

(1.05) ln (\frac{680}{980}) = ln ((\frac{680}{980})^{(1.05)})

= ln ((\frac{500}{200})^{(0.287)}) - ln ((\frac{680}{980})^{(1.05)})

Apply log rule:

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

ln ((\frac{500}{200})^{(0.287)}) - ln ((\frac{680}{980})^{(1.05)}) = ln (\frac{( \frac{500}{200} ) ^{0.287}}{( \frac{680}{980} ) ^{1.05}})

= ln (\frac{( \frac{500}{200} ) ^{0.287}}{( \frac{680}{980} ) ^{1.05}})

\frac{( \frac{500}{200} ) ^{(0.287)}}{( \frac{680}{980} ) ^{(1.05)}} = 1.90924 \dots

= ln (1.90924 \dots)

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What is (0.287)ln(500/200)-(1.05)ln(680/980) ?
The solution to (0.287)ln(500/200)-(1.05)ln(680/980) is ln(1.90924…)