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

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

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

simplify

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_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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)

Simplify

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

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

ln (e (x + 6))

4 lo g_{10} (1 0^{- 4} x 1 0^{3})

ln (\frac{563}{760})

lo g_{10} (\frac{x}{y ^{3} z})

2 ln (x) + 7 ln (z)

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