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Popular >

simplify ln((3y)/(x^5))

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

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

ln (3 y) = ln (3) + ln (y)

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

Popular Examples

join 1/14 ln(129)join

\frac{1}{14} ln (129)

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\frac{1}{5} (ln (13) - ln (3))

simplify log_{5}(x)+4log_{5}(y)-2log_{5}(z)simplify

lo g_{5} (x) + 4 lo g_{5} (y) - 2 lo g_{5} (z)

join 13/2 ln(26)join

\frac{13}{2} ln (26)

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ln (\frac{2290000}{130000})

Frequently Asked Questions (FAQ)

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