What is ln(a+b)+ln(a-b)-8ln(c) ?

The solution to ln(a+b)+ln(a-b)-8ln(c) is ln(((a+b)(a-b))/(c^8))

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simplify ln(a+b)+ln(a-b)-8ln(c)

simplify

ln (a + b) + ln (a - b) - 8 ln (c)

ln (\frac{( a + b ) ( a - b )}{c ^{8}})

Solution steps

ln (a + b) + ln (a - b) - 8 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)) - 8 ln (c)

Apply log rule:

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

8 ln (c) = ln (c^{8})

= ln ((a + b) (a - b)) - ln (c^{8})

Apply log rule:

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

ln ((a + b) (a - b)) - ln (c^{8}) = ln (\frac{( a + b ) ( a - b )}{c ^{8}})

= ln (\frac{( a + b ) ( a - b )}{c ^{8}})

ln (2 e^{2 x})

lo g_{4} (x^{2} - 36) - 5 lo g_{4} (x + 6)

lo g_{10} (\frac{x ^{3} x + 1}{( x - 2 ) ^{2}})

lo g_{3} (\frac{a b ^{2}}{3})

lo g_{3} (8 x)

What is ln(a+b)+ln(a-b)-8ln(c) ?
The solution to ln(a+b)+ln(a-b)-8ln(c) is ln(((a+b)(a-b))/(c^8))