What is log_{2}(x)+2+log_{2}(x^3)-4 ?

The solution to log_{2}(x)+2+log_{2}(x^3)-4 is 4log_{2}(x)-2

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simplify log_{2}(x)+2+log_{2}(x^3)-4

simplify

lo g_{2} (x) + 2 + lo g_{2} (x^{3}) - 4

4 lo g_{2} (x) - 2

Solution steps

lo g_{2} (x) + 2 + lo g_{2} (x^{3}) - 4

Group like terms

= lo g_{2} (x) + lo g_{2} (x^{3}) + 2 - 4

Subtract the numbers:

2 - 4 = - 2

= lo g_{2} (x) + lo g_{2} (x^{3}) - 2

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= lo g_{2} (x) + 3 lo g_{2} (x) - 2

Add similar elements:

lo g_{2} (x) + 3 lo g_{2} (x) = 4 lo g_{2} (x)

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

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What is log_{2}(x)+2+log_{2}(x^3)-4 ?
The solution to log_{2}(x)+2+log_{2}(x^3)-4 is 4log_{2}(x)-2