What is 7log_{2}(x)+4log_{2}(y)-3log_{2}(z) ?

The solution to 7log_{2}(x)+4log_{2}(y)-3log_{2}(z) is log_{2}((x^7y^4)/(z^3))

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simplify 7log_{2}(x)+4log_{2}(y)-3log_{2}(z)

simplify

7 lo g_{2} (x) + 4 lo g_{2} (y) - 3 lo g_{2} (z)

lo g_{2} (\frac{x ^{7} y ^{4}}{z ^{3}})

Solution steps

7 lo g_{2} (x) + 4 lo g_{2} (y) - 3 lo g_{2} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 lo g_{2} (x) = lo g_{2} (x^{7})

= lo g_{2} (x^{7}) + 4 lo g_{2} (y) - 3 lo g_{2} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{2} (x^{7}) + lo g_{2} (y^{4}) - 3 lo g_{2} (z)

Apply log rule:

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

lo g_{2} (x^{7}) + lo g_{2} (y^{4}) = lo g_{2} (x^{7} y^{4})

= lo g_{2} (x^{7} y^{4}) - 3 lo g_{2} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{2} (x^{7} y^{4}) - lo g_{2} (z^{3})

Apply log rule:

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

lo g_{2} (x^{7} y^{4}) - lo g_{2} (z^{3}) = lo g_{2} (\frac{x ^{7} y ^{4}}{z ^{3}})

= lo g_{2} (\frac{x ^{7} y ^{4}}{z ^{3}})

\frac{3 \cdot ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

lo g_{10} (\frac{18}{x})

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

lo g_{2} (x + 2) - lo g_{2} (x - 2)

What is 7log_{2}(x)+4log_{2}(y)-3log_{2}(z) ?
The solution to 7log_{2}(x)+4log_{2}(y)-3log_{2}(z) is log_{2}((x^7y^4)/(z^3))