What is 625ln(5)-2882/25-243/5 ln(3) ?

The solution to 625ln(5)-2882/25-243/5 ln(3) is 625ln((5^{625}*3^{2/5})/(3^{49)})-2882/25

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simplify 625ln(5)-2882/25-243/5 ln(3)

simplify

625 ln (5) - \frac{2882}{25} - \frac{243}{5} ln (3)

625 ln (\frac{5 ^{625} \cdot 3 ^{\frac{2}{5}}}{3 ^{49}}) - \frac{2882}{25}

Solution steps

625 ln (5) - \frac{2882}{25} - \frac{243}{5} ln (3)

Apply log rule:

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

\frac{243}{5} ln (3) = ln (3^{\frac{243}{5}})

= 625 ln (5) - \frac{2882}{25} - ln (3^{\frac{243}{5}})

Apply log rule:

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

ln (5) - ln (3^{\frac{243}{5}}) = ln (\frac{5}{3 ^{\frac{243}{5}}})

= 625 ln (\frac{5}{3 ^{\frac{243}{5}}}) - \frac{2882}{25}

\frac{5 ^{625}}{3 ^{\frac{243}{5}}} = \frac{5 ^{625} \cdot 3 ^{\frac{2}{5}}}{3 ^{49}}

= 625 ln (\frac{5 ^{625} \cdot 3 ^{\frac{2}{5}}}{3 ^{49}}) - \frac{2882}{25}

ln (\frac{a x}{b y})

lo g_{6} (y^{x})

ln (\frac{2 x ^{2} 2 x}{x ^{4} + ( 2 x ) ^{2}})

- lo g_{10} (9 \cdot 1 0^{- 6})

lo g_{10} (\frac{y}{x ^{9}})

What is 625ln(5)-2882/25-243/5 ln(3) ?
The solution to 625ln(5)-2882/25-243/5 ln(3) is 625ln((5^{625}*3^{2/5})/(3^{49)})-2882/25