What is ln(a+b)+5ln(a-b)-4ln(c) ?

The solution to ln(a+b)+5ln(a-b)-4ln(c) is ln(((a+b)(a-b)^5)/(c^4))

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simplify ln(a+b)+5ln(a-b)-4ln(c)

simplify

ln (a + b) + 5 ln (a - b) - 4 ln (c)

ln (\frac{( a + b ) ( a - b ) ^{5}}{c ^{4}})

Solution steps

ln (a + b) + 5 ln (a - b) - 4 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}) - 4 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}) - 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)^{5}) - 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)^{5}) - ln (c^{4}) = ln (\frac{( a - b ) ^{5} ( a + b )}{c ^{4}})

= ln (\frac{( a + b ) ( a - b ) ^{5}}{c ^{4}})

lo g_{9} (v) + 6 lo g_{9} (w) + \frac{1}{2} lo g_{9} (u)

lo g_{2} (5 n)

lo g_{10} (2 a) + lo g_{10} (b) - 2 lo g_{10} (ab)

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

lo g_{10} (\frac{x ^{3}}{2 x + 4})

What is ln(a+b)+5ln(a-b)-4ln(c) ?
The solution to ln(a+b)+5ln(a-b)-4ln(c) is ln(((a+b)(a-b)^5)/(c^4))