What is ln((3a^4b^7c)/(\sqrt[4]{b-9)}) ?

The solution to ln((3a^4b^7c)/(\sqrt[4]{b-9)}) is ln(3)+4ln(a)+7ln(b)+ln(c)-ln(\sqrt[4]{b-9})

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simplify ln((3a^4b^7c)/(\sqrt[4]{b-9)})

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln (3 a^{4} b^{7} c) = ln (3) + ln (a^{4}) + ln (b^{7}) + ln (c)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

5 ln (x) + 3 ln (y) - 4 ln (z)

lo g_{10} (6) + lo g_{10} (5) - lo g_{10} (15)

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (x)

lo g_{10} (x^{4}) y

What is ln((3a^4b^7c)/(\sqrt[4]{b-9)}) ?
The solution to ln((3a^4b^7c)/(\sqrt[4]{b-9)}) is ln(3)+4ln(a)+7ln(b)+ln(c)-ln(\sqrt[4]{b-9})