What is log_{4}((64)/(sqrt(x-1))) ?

The solution to log_{4}((64)/(sqrt(x-1))) is 3-log_{4}(sqrt(x-1))

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simplify log_{4}((64)/(sqrt(x-1)))

simplify

lo g_{4} (\frac{64}{x - 1})

3 - lo g_{4} (x - 1)

Solution steps

lo g_{4} (\frac{64}{x - 1})

Apply log rule:

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

lo g_{4} (\frac{64}{x - 1}) = lo g_{4} (64) - lo g_{4} (x - 1)

= lo g_{4} (64) - lo g_{4} (x - 1)

lo g_{4} (64) = 3

= 3 - lo g_{4} (x - 1)

lo g_{10} (15) - lo g_{10} (3)

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

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1)

lo g_{10} (10000 x)

- lo g_{10} (1.8 \times 1 0^{- 5})

What is log_{4}((64)/(sqrt(x-1))) ?
The solution to log_{4}((64)/(sqrt(x-1))) is 3-log_{4}(sqrt(x-1))