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

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

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

simplify

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

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

Solution steps

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

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

12 lo g_{10} (x) + 5 lo g_{10} (y)

ln (\frac{1}{e ^{x} + 1})

\frac{1}{3} ln (\frac{x - 1}{x + 1})

ln (\frac{0.97}{- 6})

0.3 \cdot ln (600) + 0.7 \cdot ln (28 \frac{4}{7})

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