What is 4log_{2}(x)+1/3 log_{2}(y)-5log_{2}(z) ?

The solution to 4log_{2}(x)+1/3 log_{2}(y)-5log_{2}(z) is log_{2}((x^4y^{1/3})/(z^5))

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simplify 4log_{2}(x)+1/3 log_{2}(y)-5log_{2}(z)

simplify

4 lo g_{2} (x) + \frac{1}{3} lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{2} (\frac{x ^{4} y ^{\frac{1}{3}}}{z ^{5}})

Solution steps

4 lo g_{2} (x) + \frac{1}{3} lo g_{2} (y) - 5 lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (x^{4}) + \frac{1}{3} lo g_{2} (y) - 5 lo g_{2} (z)

Apply log rule:

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

\frac{1}{3} lo g_{2} (y) = lo g_{2} (y^{\frac{1}{3}})

= lo g_{2} (x^{4}) + lo g_{2} (y^{\frac{1}{3}}) - 5 lo g_{2} (z)

Apply log rule:

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

lo g_{2} (x^{4}) + lo g_{2} (y^{\frac{1}{3}}) = lo g_{2} (x^{4} y^{\frac{1}{3}})

= lo g_{2} (x^{4} y^{\frac{1}{3}}) - 5 lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (x^{4} y^{\frac{1}{3}}) - lo g_{2} (z^{5})

Apply log rule:

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

lo g_{2} (x^{4} y^{\frac{1}{3}}) - lo g_{2} (z^{5}) = lo g_{2} (\frac{x ^{4} y ^{\frac{1}{3}}}{z ^{5}})

= lo g_{2} (\frac{x ^{4} y ^{\frac{1}{3}}}{z ^{5}})

4 lo g_{10} (x - 1) - lo g_{10} (x + 1)

ln (\frac{97}{100})

2^{2 l n (x) + l n (y)}

3 lo g_{10} (x) + 4 lo g_{10} (y) - 6 lo g_{10} (z)

2 \cdot (ln (0.07) - ln (0.06))

What is 4log_{2}(x)+1/3 log_{2}(y)-5log_{2}(z) ?
The solution to 4log_{2}(x)+1/3 log_{2}(y)-5log_{2}(z) is log_{2}((x^4y^{1/3})/(z^5))