What is expand log_{2}((6x^2)/(yz^3)) ?

The solution to expand log_{2}((6x^2)/(yz^3)) is log_{2}(6)+2log_{2}(x)-log_{2}(y)-3log_{2}(z)

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expand log_{2}((6x^2)/(yz^3))

expand

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}})

lo g_{2} (6) + 2 lo g_{2} (x) - lo g_{2} (y) - 3 lo g_{2} (z)

Solution steps

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}})

Apply log rule:

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

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}}) = lo g_{2} (6 x^{2}) - lo g_{2} (y z^{3})

= lo g_{2} (6 x^{2}) - lo g_{2} (y z^{3})

Apply log rule:

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

lo g_{2} (6 x^{2}) = lo g_{2} (6) + lo g_{2} (x^{2}), lo g_{2} (y z^{3}) = lo g_{2} (y) + lo g_{2} (z^{3})

= lo g_{2} (6) + lo g_{2} (x^{2}) - (lo g_{2} (y) + lo g_{2} (z^{3}))

Apply log rule:

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

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

= lo g_{2} (6) + 2 lo g_{2} (x) - (lo g_{2} (y) + lo g_{2} (z^{3}))

Apply log rule:

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

lo g_{2} (z^{3}) = 3 lo g_{2} (z)

= lo g_{2} (6) + 2 lo g_{2} (x) - (lo g_{2} (y) + 3 lo g_{2} (z))

- (lo g_{2} (y) + 3 lo g_{2} (z)) : - lo g_{2} (y) - 3 lo g_{2} (z)

= lo g_{2} (6) + 2 lo g_{2} (x) - lo g_{2} (y) - 3 lo g_{2} (z)

ln (\frac{ln ( e - x )}{x})

9 ln (9 x)

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

ln (\frac{2 - 5}{e ^{2} + e ^{4} + 1})

\frac{3}{4} (ln (2) - ln (\frac{3}{2}))

What is expand log_{2}((6x^2)/(yz^3)) ?
The solution to expand log_{2}((6x^2)/(yz^3)) is log_{2}(6)+2log_{2}(x)-log_{2}(y)-3log_{2}(z)