What is 112+96ln(2)-75ln(5) ?

The solution to 112+96ln(2)-75ln(5) is 112+ln((2^{96})/(5^{75)})

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simplify 112+96ln(2)-75ln(5)

simplify

112 + 96 ln (2) - 75 ln (5)

112 + ln (\frac{2 ^{96}}{5 ^{75}})

Decimal Notation

57.83428 \dots

Solution steps

112 + 96 ln (2) - 75 ln (5)

Apply log rule:

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

96 ln (2) = ln (2^{96})

= 112 + ln (2^{96}) - 75 ln (5)

Apply log rule:

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

75 ln (5) = ln (5^{75})

= 112 + ln (2^{96}) - ln (5^{75})

Apply log rule:

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

ln (2^{96}) - ln (5^{75}) = ln (\frac{2 ^{96}}{5 ^{75}})

= 112 + ln (\frac{2 ^{96}}{5 ^{75}})

lo g_{5} (2 5^{2})

ln (\frac{\frac{7}{8}}{10})

- \frac{3}{2} ln^{2} (cos (2 x))

ln (\frac{x + 3}{x})

- lo g_{10} (1.11 \cdot 1 0^{- 4})

What is 112+96ln(2)-75ln(5) ?
The solution to 112+96ln(2)-75ln(5) is 112+ln((2^{96})/(5^{75)})