What is ln(a+b)+4ln(a-b)-4ln(c) ?

The solution to ln(a+b)+4ln(a-b)-4ln(c) is ln(((a+b)(a-b)^4)/(c^4))

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simplify ln(a+b)+4ln(a-b)-4ln(c)

simplify

ln (a + b) + 4 ln (a - b) - 4 ln (c)

ln (\frac{( a + b ) ( a - b ) ^{4}}{c ^{4}})

Solution steps

ln (a + b) + 4 ln (a - b) - 4 ln (c)

Apply log rule:

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

4 ln (a - b) = ln ((a - b)^{4})

= ln (a + b) + ln ((a - b)^{4}) - 4 ln (c)

Apply log rule:

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

ln (a + b) + ln ((a - b)^{4}) = ln ((a - b)^{4} (a + b))

= ln ((a + b) (a - b)^{4}) - 4 ln (c)

Apply log rule:

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

4 ln (c) = ln (c^{4})

= ln ((a + b) (a - b)^{4}) - ln (c^{4})

Apply log rule:

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

ln ((a + b) (a - b)^{4}) - ln (c^{4}) = ln (\frac{( a - b ) ^{4} ( a + b )}{c ^{4}})

= ln (\frac{( a + b ) ( a - b ) ^{4}}{c ^{4}})

lo g_{2} (7) - lo g_{2} (3)

ln (\frac{x}{1 - x})

ln (x y z^{2})

6 lo g_{b} (x) + 7 lo g_{b} (z)

lo g_{2} (\frac{a - 1}{9})

What is ln(a+b)+4ln(a-b)-4ln(c) ?
The solution to ln(a+b)+4ln(a-b)-4ln(c) is ln(((a+b)(a-b)^4)/(c^4))