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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

3 ln (a - b) = ln ((a - b)^{3})

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

Apply log rule:

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

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

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

Apply log rule:

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

5 ln (c) = ln (c^{5})

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

Apply log rule:

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

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

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

ln (\frac{48}{45})

ln (\frac{r ^{5}}{8})

ln (y - 7) - ln (5)

ln (\frac{0.0023}{0.0001})

20 - 20 lo g_{10} (1.49 \cdot 1.5)

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