What is simplify-4ln(a)+9ln(b) ?

The solution to simplify-4ln(a)+9ln(b) is ln((b^9)/(a^4))

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simplify-4ln(a)+9ln(b)

simplify

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

ln (\frac{b ^{9}}{a ^{4}})

Solution steps

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

Apply log rule:

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

4 ln (a) = ln (a^{4})

= - ln (a^{4}) + 9 ln (b)

Apply log rule:

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

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

= - ln (a^{4}) + ln (b^{9})

Apply log rule:

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

ln (b^{9}) - ln (a^{4}) = ln (\frac{b ^{9}}{a ^{4}})

= ln (\frac{b ^{9}}{a ^{4}})

lo g_{6} (\frac{36 y}{x ^{7} z ^{2}})

ln (x^{y}) + ln (y^{x})

lo g_{4} (\frac{x z}{16 y ^{2}})

ln (\frac{4}{6}) - ln (\frac{1}{3})

f (x) = ln (\frac{3}{3 - x})

What is simplify-4ln(a)+9ln(b) ?
The solution to simplify-4ln(a)+9ln(b) is ln((b^9)/(a^4))