What is expand ln((5x)/(y^2)) ?

The solution to expand ln((5x)/(y^2)) is ln(5)+ln(x)-2ln(y)

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expand ln((5x)/(y^2))

expand

ln (\frac{5 x}{y ^{2}})

ln (5) + ln (x) - 2 ln (y)

Solution steps

ln (\frac{5 x}{y ^{2}})

Apply log rule:

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

ln (\frac{5 x}{y ^{2}}) = ln (5 x) - ln (y^{2})

= ln (5 x) - ln (y^{2})

Apply log rule:

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

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

= ln (5 x) - 2 ln (y)

Apply log rule:

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

ln (5 x) = ln (5) + ln (x)

= ln (5) + ln (x) - 2 ln (y)

\frac{1}{3} ln (\frac{1}{27})

ln (3 x) + 1

lo g_{e} (22)

5 lo g_{7} (a) + 10 lo g_{7} (b)

ln (3 x) + ln (2 x^{2})

What is expand ln((5x)/(y^2)) ?
The solution to expand ln((5x)/(y^2)) is ln(5)+ln(x)-2ln(y)