What is log_{4}((sqrt(c))/(64)) ?

The solution to log_{4}((sqrt(c))/(64)) is log_{4}(sqrt(c))-3

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simplify log_{4}((sqrt(c))/(64))

simplify

lo g_{4} (\frac{c}{64})

lo g_{4} (c) - 3

Solution steps

lo g_{4} (\frac{c}{64})

Apply log rule:

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

lo g_{4} (\frac{c}{64}) = lo g_{4} (c) - lo g_{4} (64)

= lo g_{4} (c) - lo g_{4} (64)

lo g_{4} (64) = 3

= lo g_{4} (c) - 3

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - (\frac{1}{4}) lo g_{2} (\frac{1}{4})

2 ln (x) - 3 ln (y) - 4 ln (z)

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

lo g_{10} (27) - lo g_{10} (9)

2 lo g_{10} (3) - 3 lo g_{10} (2)

What is log_{4}((sqrt(c))/(64)) ?
The solution to log_{4}((sqrt(c))/(64)) is log_{4}(sqrt(c))-3