What is 7ln(x+9)-8ln(x) ?

The solution to 7ln(x+9)-8ln(x) is ln(((x+9)^7)/(x^8))

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simplify 7ln(x+9)-8ln(x)

simplify

7 ln (x + 9) - 8 ln (x)

ln (\frac{( x + 9 ) ^{7}}{x ^{8}})

Solution steps

7 ln (x + 9) - 8 ln (x)

Apply log rule:

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

7 ln (x + 9) = ln ((x + 9)^{7})

= ln ((x + 9)^{7}) - 8 ln (x)

Apply log rule:

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

8 ln (x) = ln (x^{8})

= ln ((x + 9)^{7}) - ln (x^{8})

Apply log rule:

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

ln ((x + 9)^{7}) - ln (x^{8}) = ln (\frac{( x + 9 ) ^{7}}{x ^{8}})

= ln (\frac{( x + 9 ) ^{7}}{x ^{8}})

ln (\frac{y}{x} - 4) + 6 (\frac{1}{5} ln (\frac{y}{x} - 1) - \frac{1}{5} ln (\frac{y}{x} + 4)) + ln (x)

\frac{3}{8} \cdot ln (\frac{8}{3}) + (\frac{5}{16} \cdot ln (\frac{16}{5})) \cdot 2

ln (\frac{1}{d}) - ln (\frac{1}{y})

ln (\frac{3 x - 4}{2 x + 1})

(\frac{1}{2} lo g_{e} (9 x^{2})) + lo g_{e} (3 x)

What is 7ln(x+9)-8ln(x) ?
The solution to 7ln(x+9)-8ln(x) is ln(((x+9)^7)/(x^8))