What is expand log_{2}(((2x^6))/y) ?

The solution to expand log_{2}(((2x^6))/y) is 1+6log_{2}(x)-log_{2}(y)

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expand log_{2}(((2x^6))/y)

expand

lo g_{2} (\frac{( 2 x ^{6} )}{y})

1 + 6 lo g_{2} (x) - lo g_{2} (y)

Solution steps

lo g_{2} (\frac{( 2 x ^{6} )}{y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{( 2 x ^{6} )}{y}) = lo g_{2} ((2 x^{6})) - lo g_{2} (y)

= lo g_{2} (2 x^{6}) - lo g_{2} (y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{2} (2 x^{6}) = lo g_{2} (2) + lo g_{2} (x^{6})

= lo g_{2} (2) + lo g_{2} (x^{6}) - lo g_{2} (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{2} (x^{6}) = 6 lo g_{2} (x)

= lo g_{2} (2) + 6 lo g_{2} (x) - lo g_{2} (y)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 6 lo g_{2} (x) - lo g_{2} (y)

lo g_{a} (x^{2} - 4) - lo g_{a} (x - 2)

lo g_{4} (\frac{5 x}{y})

lo g_{10} (1000000 y)

lo g_{3} (11 x (3 x + 4))

ln (x^{11} 2 - x)

What is expand log_{2}(((2x^6))/y) ?
The solution to expand log_{2}(((2x^6))/y) is 1+6log_{2}(x)-log_{2}(y)