What is 40002+103ln(103)-105ln(105) ?

The solution to 40002+103ln(103)-105ln(105) is 40002+ln((103^{103})/(105^{105)})

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simplify 40002+103ln(103)-105ln(105)

simplify

40002 + 103 ln (103) - 105 ln (105)

40002 + ln (\frac{10 3 ^{103}}{10 5 ^{105}})

Decimal Notation

39990.71124 \dots

Solution steps

40002 + 103 ln (103) - 105 ln (105)

Apply log rule:

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

103 ln (103) = ln (10 3^{103})

= 40002 + ln (10 3^{103}) - 105 ln (105)

Apply log rule:

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

105 ln (105) = ln (10 5^{105})

= 40002 + ln (10 3^{103}) - ln (10 5^{105})

Apply log rule:

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

ln (10 3^{103}) - ln (10 5^{105}) = ln (\frac{10 3 ^{103}}{10 5 ^{105}})

= 40002 + ln (\frac{10 3 ^{103}}{10 5 ^{105}})

ln (6) + ln (21) - ln (7)

ln (\frac{z}{x ^{6} y})

ln (\frac{273.31}{373.15})

ln (0.2 x)

2 ln (\frac{- 1}{e}) + 2

What is 40002+103ln(103)-105ln(105) ?
The solution to 40002+103ln(103)-105ln(105) is 40002+ln((103^{103})/(105^{105)})