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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

3 ln (x) + ln (y)

lo g_{4} (\frac{16}{x + 2})

3 lo g_{b} (5) + lo g_{b} (2) - lo g_{b} (10)

lo g_{10} (\frac{x a ^{2}}{y ^{7}})

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