What is log_{4}((64a)/(b^4)) ?

The solution to log_{4}((64a)/(b^4)) is 3+log_{4}(a)-4log_{4}(b)

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simplify log_{4}((64a)/(b^4))

simplify

lo g_{4} (\frac{64 a}{b ^{4}})

3 + lo g_{4} (a) - 4 lo g_{4} (b)

Solution steps

lo g_{4} (\frac{64 a}{b ^{4}})

Apply log rule:

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

lo g_{4} (\frac{64 a}{b ^{4}}) = lo g_{4} (64 a) - lo g_{4} (b^{4})

= lo g_{4} (64 a) - lo g_{4} (b^{4})

lo g_{4} (64 a) = 3 + lo g_{4} (a)

lo g_{4} (b^{4}) = 4 lo g_{4} (b)

= 3 + lo g_{4} (a) - 4 lo g_{4} (b)

lo g_{10} (45) + lo g_{10} (\frac{1}{9})

lo g_{10} (\frac{x}{1000 y ^{6}})

3 lo g_{10} (x^{4}) - 5 lo g_{10} (x^{2})

2 (ln (3) - ln (2))

lo g_{b} (x^{2} y^{3} z)

What is log_{4}((64a)/(b^4)) ?
The solution to log_{4}((64a)/(b^4)) is 3+log_{4}(a)-4log_{4}(b)