What is expand log_{4}((a^9)/b) ?

The solution to expand log_{4}((a^9)/b) is 9log_{4}(a)-log_{4}(b)

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expand log_{4}((a^9)/b)

expand

lo g_{4} (\frac{a ^{9}}{b})

9 lo g_{4} (a) - lo g_{4} (b)

Solution steps

lo g_{4} (\frac{a ^{9}}{b})

Apply log rule:

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

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

= lo g_{4} (a^{9}) - lo g_{4} (b)

Apply log rule:

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

lo g_{4} (a^{9}) = 9 lo g_{4} (a)

= 9 lo g_{4} (a) - lo g_{4} (b)

- lo g_{10} (8.24 \cdot 1 0^{- 3})

ln (- 2 e)

ln (\frac{1}{x ^{2}})

- lo g_{10} (4.6 \cdot 1 0^{- 4})

- ln ∣ v + 1 ∣ + ln ∣ v - 1 ∣ - \frac{1}{2} ln v^{2} - 1

What is expand log_{4}((a^9)/b) ?
The solution to expand log_{4}((a^9)/b) is 9log_{4}(a)-log_{4}(b)