What is ln(x+y)+ln(x-y)-2ln(z) ?

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

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simplify ln(x+y)+ln(x-y)-2ln(z)

simplify

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

ln (\frac{( x + y ) ( x - y )}{z ^{2}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{e} (4 x)

ln (\frac{1}{2} x^{2} - 4)

- ln ∣ x - 3 ∣ + 2 ln ∣ x - 2 ∣ + C

ln (\frac{x ^{4}}{y ^{5}})

\frac{1}{2} ln (4 + 15)

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