What is ln(a+b)+ln(a-b)-7ln(c) ?

The solution to ln(a+b)+ln(a-b)-7ln(c) is ln(((a+b)(a-b))/(c^7))

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simplify ln(a+b)+ln(a-b)-7ln(c)

simplify

ln (a + b) + ln (a - b) - 7 ln (c)

ln (\frac{( a + b ) ( a - b )}{c ^{7}})

Solution steps

ln (a + b) + ln (a - b) - 7 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)) - 7 ln (c)

Apply log rule:

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

7 ln (c) = ln (c^{7})

= ln ((a + b) (a - b)) - ln (c^{7})

Apply log rule:

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

ln ((a + b) (a - b)) - ln (c^{7}) = ln (\frac{( a + b ) ( a - b )}{c ^{7}})

= ln (\frac{( a + b ) ( a - b )}{c ^{7}})

lo g_{7} (\frac{x ^{12}}{x - 3})

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

ln (\frac{3}{4 x ^{4} y})

lo g_{2} (5) + lo g_{2} (x) - lo g_{2} (3)

lo g_{10} (5 t)

What is ln(a+b)+ln(a-b)-7ln(c) ?
The solution to ln(a+b)+ln(a-b)-7ln(c) is ln(((a+b)(a-b))/(c^7))