What is 4log_{2}(a)+6log_{2}(b) ?

The solution to 4log_{2}(a)+6log_{2}(b) is log_{2}(a^4b^6)

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simplify 4log_{2}(a)+6log_{2}(b)

simplify

4 lo g_{2} (a) + 6 lo g_{2} (b)

lo g_{2} (a^{4} b^{6})

Solution steps

4 lo g_{2} (a) + 6 lo g_{2} (b)

Apply log rule:

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

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

= lo g_{2} (a^{4}) + 6 lo g_{2} (b)

Apply log rule:

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

6 lo g_{2} (b) = lo g_{2} (b^{6})

= lo g_{2} (a^{4}) + lo g_{2} (b^{6})

Apply log rule:

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

lo g_{2} (a^{4}) + lo g_{2} (b^{6}) = lo g_{2} (a^{4} b^{6})

= lo g_{2} (a^{4} b^{6})

ln (\frac{1}{c})

- lo g_{10} (1.18 \cdot 1 0^{- 3})

ln (x) + 2 ln (y) + ln (8 - z)

- ln (1.8 \cdot 1 0^{- 5})

4 ln (5 x)

What is 4log_{2}(a)+6log_{2}(b) ?
The solution to 4log_{2}(a)+6log_{2}(b) is log_{2}(a^4b^6)