What is ln(9/(2x^2y)) ?

The solution to ln(9/(2x^2y)) is 2ln(3)-ln(2)-2ln(x)-ln(y)

Popular >

simplify ln(9/(2x^2y))

simplify

ln (\frac{9}{2 x ^{2} y})

2 ln (3) - ln (2) - 2 ln (x) - ln (y)

Solution steps

ln (\frac{9}{2 x ^{2} y})

Apply log rule:

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

ln (\frac{9}{2 x ^{2} y}) = ln (9) - ln (2 x^{2} y)

= ln (9) - 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 (9) - (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 (9) - (ln (2) + 2 ln (x) + ln (y))

ln (9) = 2 ln (3)

= 2 ln (3) - (2 ln (x) + ln (y) + ln (2))

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

= 2 ln (3) - ln (2) - 2 ln (x) - ln (y)

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (z)

\frac{1}{3} ln (x) + 3 ln (y)

lo g_{6} (x) + lo g_{6} (y) + 6 lo g_{6} (z)

lo g_{2} (x + 1) + lo g_{2} (x - 1)

\frac{1}{3} lo g_{2} (5)

What is ln(9/(2x^2y)) ?
The solution to ln(9/(2x^2y)) is 2ln(3)-ln(2)-2ln(x)-ln(y)