What is 5log_{2}(x)-3log_{2}(z) ?

The solution to 5log_{2}(x)-3log_{2}(z) is log_{2}((x^5)/(z^3))

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simplify 5log_{2}(x)-3log_{2}(z)

simplify

5 lo g_{2} (x) - 3 lo g_{2} (z)

lo g_{2} (\frac{x ^{5}}{z ^{3}})

Solution steps

5 lo g_{2} (x) - 3 lo g_{2} (z)

Apply log rule:

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

5 lo g_{2} (x) = lo g_{2} (x^{5})

= lo g_{2} (x^{5}) - 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^{5}) - 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^{5}) - lo g_{2} (z^{3}) = lo g_{2} (\frac{x ^{5}}{z ^{3}})

= lo g_{2} (\frac{x ^{5}}{z ^{3}})

ln (5 x^{4} y)

ln (\frac{x + 2 y}{3 + x z})

ln ((\frac{a}{b})^{n} (x)^{n (a - b)})

ln (\frac{168.9 2 ^{n} 437.8 4 ^{m}}{146. 2 ^{n} 392. 2 ^{m}})

\frac{1}{4} (ln (14) - ln (5))

What is 5log_{2}(x)-3log_{2}(z) ?
The solution to 5log_{2}(x)-3log_{2}(z) is log_{2}((x^5)/(z^3))