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_{2} \frac{3 x ^{2}}{2 ( a y ^{5} )}

ln (x yz) + (i + j + k)

ln (2 e) \cdot \frac{3}{59}

lo g_{10} (8) + lo g_{10} (5) + lo g_{10} (3)

lo g_{6} (36 x^{3})

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)