What is ln(3)+5ln(x)-ln(y) ?

The solution to ln(3)+5ln(x)-ln(y) is ln((3x^5)/y)

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simplify ln(3)+5ln(x)-ln(y)

simplify

ln (3) + 5 ln (x) - ln (y)

ln (\frac{3 x ^{5}}{y})

Solution steps

ln (3) + 5 ln (x) - ln (y)

Apply log rule:

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

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

= ln (3) + ln (x^{5}) - ln (y)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (3) + ln (x^{5}) = ln (3 x^{5})

= ln (3 x^{5}) - ln (y)

Apply log rule:

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

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

= ln (\frac{3 x ^{5}}{y})

ln (\frac{x ^{2} + 1 - x}{x ^{2} - 1 + x})

0.5 (- \frac{3}{5} lo g_{2} (\frac{3}{5}) - \frac{2}{5} lo g_{2} (\frac{2}{5}))

(\frac{( ln ( x ) - ln ( 100 ) )}{2 \cdot ln ( 2 )})^{2}

ln (6) + ln (18) - ln (3) + 3 ln (6)

ln (\frac{100}{5})