What is ln(a+b)+ln(a-b)-6ln(c) ?

The solution to ln(a+b)+ln(a-b)-6ln(c) is ln(((a+b)(a-b))/(c^6))

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simplify ln(a+b)+ln(a-b)-6ln(c)

simplify

ln (a + b) + ln (a - b) - 6 ln (c)

ln (\frac{( a + b ) ( a - b )}{c ^{6}})

Solution steps

ln (a + b) + ln (a - b) - 6 ln (c)

Apply log rule:

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

ln (a + b) + ln (a - b) = ln ((a + b) (a - b))

= ln ((a + b) (a - b)) - 6 ln (c)

Apply log rule:

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

6 ln (c) = ln (c^{6})

= ln ((a + b) (a - b)) - ln (c^{6})

Apply log rule:

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

ln ((a + b) (a - b)) - ln (c^{6}) = ln (\frac{( a + b ) ( a - b )}{c ^{6}})

= ln (\frac{( a + b ) ( a - b )}{c ^{6}})

lo g_{10} (2) + lo g_{10} (3) + lo g_{10} (4)

\frac{2}{3} ln (x) - \frac{1}{2} ln (y)

ln (\frac{1}{x ^{n}})

lo g_{3} (6) - lo g_{3} (4)

lo g_{10} (\frac{6}{x})

What is ln(a+b)+ln(a-b)-6ln(c) ?
The solution to ln(a+b)+ln(a-b)-6ln(c) is ln(((a+b)(a-b))/(c^6))