What is ln(a+b)+5ln(a-b)-3ln(c) ?

The solution to ln(a+b)+5ln(a-b)-3ln(c) is ln(((a+b)(a-b)^5)/(c^3))

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simplify ln(a+b)+5ln(a-b)-3ln(c)

simplify

ln (a + b) + 5 ln (a - b) - 3 ln (c)

ln (\frac{( a + b ) ( a - b ) ^{5}}{c ^{3}})

Solution steps

ln (a + b) + 5 ln (a - b) - 3 ln (c)

Apply log rule:

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

5 ln (a - b) = ln ((a - b)^{5})

= ln (a + b) + ln ((a - b)^{5}) - 3 ln (c)

Apply log rule:

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

ln (a + b) + ln ((a - b)^{5}) = ln ((a - b)^{5} (a + b))

= ln ((a + b) (a - b)^{5}) - 3 ln (c)

Apply log rule:

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

3 ln (c) = ln (c^{3})

= ln ((a + b) (a - b)^{5}) - ln (c^{3})

Apply log rule:

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

ln ((a + b) (a - b)^{5}) - ln (c^{3}) = ln (\frac{( a - b ) ^{5} ( a + b )}{c ^{3}})

= ln (\frac{( a + b ) ( a - b ) ^{5}}{c ^{3}})

ln (2) + 5 ln (x) - 7 ln (y)

3 lo g_{c} (x) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

lo g_{10} (2) + lo g_{10} (125)

ln ((8 x)^{\frac{1}{2}}) + ln (4) x^{2} - ln ((16 x)^{\frac{1}{2}})

lo g_{10} (\frac{x + y}{z})

What is ln(a+b)+5ln(a-b)-3ln(c) ?
The solution to ln(a+b)+5ln(a-b)-3ln(c) is ln(((a+b)(a-b)^5)/(c^3))