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

The solution to ln(x+y)+ln(x-y)-2ln(2) is ln(((x+y)(x-y))/4)

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

simplify

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

ln (\frac{( x + y ) ( x - y )}{4})

Solution steps

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

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 (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} = 4

= ln (\frac{( x + y ) ( x - y )}{4})

lo g_{10} ((\frac{a ^{3}}{b})^{5})

2 lo g_{N} (711.9) - lo g_{N} (7888.995)

ln (3 x^{6})

\frac{1}{2} ln ∣ 2 (8.5) + 1 ∣ + 2 ln ∣ 8.5 - 1 ∣ + c

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

What is ln(x+y)+ln(x-y)-2ln(2) ?
The solution to ln(x+y)+ln(x-y)-2ln(2) is ln(((x+y)(x-y))/4)