What is 3*log_{2}(p)+7*log_{2}(q) ?

The solution to 3*log_{2}(p)+7*log_{2}(q) is log_{2}(p^3q^7)

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simplify 3log_{2}(p)+7log_{2}(q)

simplify

3 \cdot lo g_{2} (p) + 7 \cdot lo g_{2} (q)

lo g_{2} (p^{3} q^{7})

Solution steps

3 lo g_{2} (p) + 7 lo g_{2} (q)

Apply log rule:

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

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

= lo g_{2} (p^{3}) + 7 lo g_{2} (q)

Apply log rule:

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

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

= lo g_{2} (p^{3}) + lo g_{2} (q^{7})

Apply log rule:

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

lo g_{2} (p^{3}) + lo g_{2} (q^{7}) = lo g_{2} (p^{3} q^{7})

= lo g_{2} (p^{3} q^{7})

lo g_{7} (x) - lo g_{7} (x^{8})

2 lo g_{10} (x) - lo g_{10} (x - 1)

- lo g_{10} (6.8 \cdot 1 0^{- 4})

ln (\frac{x}{e ^{6 x}})

lo g_{10} (1 y)

What is 3*log_{2}(p)+7*log_{2}(q) ?
The solution to 3*log_{2}(p)+7*log_{2}(q) is log_{2}(p^3q^7)