What is 14+7ln(14x-7)-7ln(7x+1) ?

The solution to 14+7ln(14x-7)-7ln(7x+1) is 14+ln(((14x-7)^7)/((7x+1)^7))

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simplify 14+7ln(14x-7)-7ln(7x+1)

simplify

14 + 7 ln (14 x - 7) - 7 ln (7 x + 1)

14 + ln (\frac{( 14 x - 7 ) ^{7}}{( 7 x + 1 ) ^{7}})

Solution steps

14 + 7 ln (14 x - 7) - 7 ln (7 x + 1)

Apply log rule:

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

7 ln (14 x - 7) = ln ((14 x - 7)^{7})

= 14 + ln ((14 x - 7)^{7}) - 7 ln (7 x + 1)

Apply log rule:

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

7 ln (7 x + 1) = ln ((7 x + 1)^{7})

= 14 + ln ((14 x - 7)^{7}) - ln ((7 x + 1)^{7})

Apply log rule:

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

ln ((14 x - 7)^{7}) - ln ((7 x + 1)^{7}) = ln (\frac{( 14 x - 7 ) ^{7}}{( 7 x + 1 ) ^{7}})

= 14 + ln (\frac{( 14 x - 7 ) ^{7}}{( 7 x + 1 ) ^{7}})

\frac{1}{2} lo g_{10} (b) + 9 lo g_{10} (c)

ln (\frac{2}{x})

ln (x^{6}) - ln (x)

lo g_{x} ((a) (4))

lo g_{a} (\frac{M}{N})

What is 14+7ln(14x-7)-7ln(7x+1) ?
The solution to 14+7ln(14x-7)-7ln(7x+1) is 14+ln(((14x-7)^7)/((7x+1)^7))