What is ln(9)+9ln(x)-6ln(y) ?

The solution to ln(9)+9ln(x)-6ln(y) is ln((9x^9)/(y^6))

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simplify ln(9)+9ln(x)-6ln(y)

simplify

ln (9) + 9 ln (x) - 6 ln (y)

ln (\frac{9 x ^{9}}{y ^{6}})

Solution steps

ln (9) + 9 ln (x) - 6 ln (y)

Apply log rule:

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

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

= ln (9) + ln (x^{9}) - 6 ln (y)

Apply log rule:

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

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

= ln (9 x^{9}) - 6 ln (y)

Apply log rule:

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

6 ln (y) = ln (y^{6})

= ln (9 x^{9}) - ln (y^{6})

Apply log rule:

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

ln (9 x^{9}) - ln (y^{6}) = ln (\frac{9 x ^{9}}{y ^{6}})

= ln (\frac{9 x ^{9}}{y ^{6}})

- lo g_{10} (1.7 \cdot 1 0^{- 8})

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

ln (x^{7} (x + 9)^{5} (x^{2} + 9)^{7})

ln (t) + 7 ln (r) - 6 ln (t)

2 (1 - ln (3) + ln (2))

What is ln(9)+9ln(x)-6ln(y) ?
The solution to ln(9)+9ln(x)-6ln(y) is ln((9x^9)/(y^6))