What is ln((y^2)/(2y)) ?

The solution to ln((y^2)/(2y)) is ln(y)-ln(2)

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simplify ln((y^2)/(2y))

simplify

ln (\frac{y ^{2}}{2 y})

ln (y) - ln (2)

Solution steps

ln (\frac{y ^{2}}{2 y})

Apply log rule:

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

ln (\frac{y ^{2}}{2 y}) = ln (y^{2}) - ln (2 y)

= ln (y^{2}) - ln (2 y)

Apply log rule:

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

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

= 2 ln (y) - ln (2 y)

Apply log rule:

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

ln (2 y) = ln (2) + ln (y)

= 2 ln (y) - (ln (y) + ln (2))

- (ln (2) + ln (y)) : - ln (2) - ln (y)

= 2 ln (y) - ln (2) - ln (y)

Simplify

2 ln (y) - ln (2) - ln (y) : ln (y) - ln (2)

= ln (y) - ln (2)

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lo g_{9} (7 \cdot 5 \cdot 1 2^{5})

lo g_{8} ((\frac{u ^{6}}{v})^{4})

ln (\frac{3 x - 5}{2 x + 1})

ln ((x^{4} + 5) (x^{2} - 1)^{2})