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(0.88624…)

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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 (0.88624 \dots)

Decimal Notation

- 0.12075 \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} (ab)

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

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

(\frac{500}{200})^{(0.287)} (\frac{680}{980})^{(1.05)} = 0.88624 \dots

= ln (0.88624 \dots)

ln (\frac{0.42}{- 0.23})

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20 lo g_{10} (\frac{4 π}{3 \cdot 1 0 ^{8}})

ln (x^{4}) + ln (x^{5})

- lo g_{10} (2.7 \cdot 1 0^{- 11})

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(0.88624…)