What is ln(a+b)+ln(a-b)-9ln(c) ?

The solution to ln(a+b)+ln(a-b)-9ln(c) is ln(((a+b)(a-b))/(c^9))

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simplify ln(a+b)+ln(a-b)-9ln(c)

simplify

ln (a + b) + ln (a - b) - 9 ln (c)

ln (\frac{( a + b ) ( a - b )}{c ^{9}})

Solution steps

ln (a + b) + ln (a - b) - 9 ln (c)

Apply log rule:

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

ln (a + b) + ln (a - b) = ln ((a + b) (a - b))

= ln ((a + b) (a - b)) - 9 ln (c)

Apply log rule:

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

9 ln (c) = ln (c^{9})

= ln ((a + b) (a - b)) - ln (c^{9})

Apply log rule:

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

ln ((a + b) (a - b)) - ln (c^{9}) = ln (\frac{( a + b ) ( a - b )}{c ^{9}})

= ln (\frac{( a + b ) ( a - b )}{c ^{9}})

lo g_{2} (\frac{x ^{3}}{x - 3})

4 [ln (z) + ln (z + 5)] - 2 ln (z - 5)

ln (x^{2} y)

lo g_{5} (\frac{14 x}{y})

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

What is ln(a+b)+ln(a-b)-9ln(c) ?
The solution to ln(a+b)+ln(a-b)-9ln(c) is ln(((a+b)(a-b))/(c^9))