What is log_{2}((x^4)/(2y)) ?

The solution to log_{2}((x^4)/(2y)) is 4log_{2}(x)-1-log_{2}(y)

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simplify log_{2}((x^4)/(2y))

simplify

lo g_{2} (\frac{x ^{4}}{2 y})

4 lo g_{2} (x) - 1 - lo g_{2} (y)

Solution steps

lo g_{2} (\frac{x ^{4}}{2 y})

Apply log rule:

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

lo g_{2} (\frac{x ^{4}}{2 y}) = lo g_{2} (x^{4}) - lo g_{2} (2 y)

= lo g_{2} (x^{4}) - lo g_{2} (2 y)

lo g_{2} (x^{4}) = 4 lo g_{2} (x)

lo g_{2} (2 y) = 1 + lo g_{2} (y)

= 4 lo g_{2} (x) - (1 + lo g_{2} (y))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{2} (y)) = - 1 - lo g_{2} (y)

= 4 lo g_{2} (x) - 1 - lo g_{2} (y)

ln (r i g h t)

lo g_{b} (b^{13}) + lo g_{b} (1)

lo g_{7} (12) - lo g_{7} (2)

lo g_{10} (x^{2} - 2 x - 15) - lo g_{10} (x + 3)

lo g_{3} (\frac{x}{27})

What is log_{2}((x^4)/(2y)) ?
The solution to log_{2}((x^4)/(2y)) is 4log_{2}(x)-1-log_{2}(y)