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

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

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

simplify

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

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

Solution steps

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

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 (a)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln ((e^{z} x^{2} y)^{3})

(ln (3 e))^{2} - 3 ln (3 e)

ln (9) + 4 ln (4)

ln (x x^{2} + 2)

ln (\frac{e ^{3}}{n})

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