What is 200ln((400)/(500-300)) ?

The solution to 200ln((400)/(500-300)) is 200(2ln(20)-ln(200))

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simplify 200ln((400)/(500-300))

simplify

200 ln (\frac{400}{500 - 300})

200 (2 ln (20) - ln (200))

Decimal Notation

138.62943 \dots

Solution steps

200 ln (\frac{400}{500 - 300})

Apply log rule:

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

ln (\frac{400}{500 - 300}) = ln (400) - ln (500 - 300)

= 200 (ln (400) - ln (500 - 300))

Subtract the numbers:

500 - 300 = 200

= 200 (ln (400) - ln (200))

ln (400) = 2 ln (20)

= 200 (2 ln (20) - ln (200))

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What is 200ln((400)/(500-300)) ?
The solution to 200ln((400)/(500-300)) is 200(2ln(20)-ln(200))