What is log_{2}((x^9)/(5y)) ?

The solution to log_{2}((x^9)/(5y)) is 9log_{2}(x)-log_{2}(5)-log_{2}(y)

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simplify log_{2}((x^9)/(5y))

simplify

lo g_{2} (\frac{x ^{9}}{5 y})

9 lo g_{2} (x) - lo g_{2} (5) - lo g_{2} (y)

Solution steps

lo g_{2} (\frac{x ^{9}}{5 y})

Apply log rule:

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

lo g_{2} (\frac{x ^{9}}{5 y}) = lo g_{2} (x^{9}) - lo g_{2} (5 y)

= lo g_{2} (x^{9}) - lo g_{2} (5 y)

lo g_{2} (x^{9}) = 9 lo g_{2} (x)

lo g_{2} (5 y) = lo g_{2} (5) + lo g_{2} (y)

= 9 lo g_{2} (x) - (lo g_{2} (5) + lo g_{2} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (5) + lo g_{2} (y)) = - lo g_{2} (5) - lo g_{2} (y)

= 9 lo g_{2} (x) - lo g_{2} (5) - lo g_{2} (y)

lo g_{2} (6) + lo g_{2} (7)

lo g_{2} (6) + lo g_{2} (9)

- lo g_{10} (6.3 \times 1 0^{- 8})

lo g_{10} (4) + lo g_{10} (6)

ln ∣ 4 x + 1 ∣ - ln ∣ x + 1 ∣ + C

What is log_{2}((x^9)/(5y)) ?
The solution to log_{2}((x^9)/(5y)) is 9log_{2}(x)-log_{2}(5)-log_{2}(y)