What is 1004*ln(100/930)-287*ln(3/4) ?

The solution to 1004*ln(100/930)-287*ln(3/4) is 1004ln((2^{1578}*5^{1004})/(3^{1291)*31^{1004}})

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simplify 1004ln(100/930)-287ln(3/4)

simplify

1004 \cdot ln (\frac{100}{930}) - 287 \cdot ln (\frac{3}{4})

1004 ln (\frac{2 ^{1578} \cdot 5 ^{1004}}{3 ^{1291} \cdot 3 1 ^{1004}})

Solution steps

1004 ln (\frac{100}{930}) - 287 ln (\frac{3}{4})

Apply log rule:

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

287 ln (\frac{3}{4}) = ln ((\frac{3}{4})^{287})

= 1004 ln (\frac{100}{930}) - ln ((\frac{3}{4})^{287})

Apply log rule:

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

ln (\frac{100}{930}) - ln ((\frac{3}{4})^{287}) = ln (\frac{\frac{100}{930}}{( \frac{3}{4} ) ^{287}})

= 1004 ln (\frac{\frac{100}{930}}{( \frac{3}{4} ) ^{287}})

Simplify

\frac{( \frac{100}{930} ) ^{1004}}{( \frac{3}{4} ) ^{287}} : \frac{2 ^{1578} \cdot 5 ^{1004}}{3 ^{1291} \cdot 3 1 ^{1004}}

= 1004 ln (\frac{2 ^{1578} \cdot 5 ^{1004}}{3 ^{1291} \cdot 3 1 ^{1004}})

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What is 1004*ln(100/930)-287*ln(3/4) ?
The solution to 1004*ln(100/930)-287*ln(3/4) is 1004ln((2^{1578}*5^{1004})/(3^{1291)*31^{1004}})