What is 1/3 (log_{2}(c)+log_{2}(d))-4log_{2}(e) ?

The solution to 1/3 (log_{2}(c)+log_{2}(d))-4log_{2}(e) is log_{2}(((cd)^{1/3})/(e^4))

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simplify 1/3 (log_{2}(c)+log_{2}(d))-4log_{2}(e)

simplify

\frac{1}{3} (lo g_{2} (c) + lo g_{2} (d)) - 4 lo g_{2} (e)

lo g_{2} (\frac{( c d ) ^{\frac{1}{3}}}{e ^{4}})

Solution steps

\frac{1}{3} (lo g_{2} (c) + lo g_{2} (d)) - 4 lo g_{2} (e)

Apply log rule:

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

lo g_{2} (c) + lo g_{2} (d) = lo g_{2} (c d)

= \frac{1}{3} lo g_{2} (c d) - 4 lo g_{2} (e)

Apply log rule:

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

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

= lo g_{2} ((c d)^{\frac{1}{3}}) - 4 lo g_{2} (e)

Apply log rule:

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

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

= lo g_{2} ((c d)^{\frac{1}{3}}) - lo g_{2} (e^{4})

Apply log rule:

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

lo g_{2} ((c d)^{\frac{1}{3}}) - lo g_{2} (e^{4}) = lo g_{2} (\frac{( c d ) ^{\frac{1}{3}}}{e ^{4}})

= lo g_{2} (\frac{( c d ) ^{\frac{1}{3}}}{e ^{4}})

lo g_{w} (\frac{9 x}{5})

lo g_{10} (x \cdot y \cdot z^{5})

(lo g_{c} (x) - lo g_{c} (y)) + 5 lo g_{c} (v)

1 + lo g_{10} (a) - \frac{1}{2} lo g_{10} (b)

lo g_{10} (\frac{( 100 x ) ^{2}}{27})

What is 1/3 (log_{2}(c)+log_{2}(d))-4log_{2}(e) ?
The solution to 1/3 (log_{2}(c)+log_{2}(d))-4log_{2}(e) is log_{2}(((cd)^{1/3})/(e^4))