What is log_{10}(8)-log_{10}(2)+2log_{10}(w) ?

The solution to log_{10}(8)-log_{10}(2)+2log_{10}(w) is log_{10}(4w^2)

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simplify log_{10}(8)-log_{10}(2)+2log_{10}(w)

simplify

lo g_{10} (8) - lo g_{10} (2) + 2 lo g_{10} (w)

lo g_{10} (4 w^{2})

Solution steps

lo g_{10} (8) - lo g_{10} (2) + 2 lo g_{10} (w)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{10} (w) = lo g_{10} (w^{2})

= lo g_{10} (8) - lo g_{10} (2) + lo g_{10} (w^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (8) - lo g_{10} (2) = lo g_{10} (\frac{8}{2})

= lo g_{10} (\frac{8}{2}) + lo g_{10} (w^{2})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{8}{2}) + lo g_{10} (w^{2}) = lo g_{10} (\frac{8}{2} w^{2})

= lo g_{10} (\frac{8}{2} w^{2})

Simplify

\frac{8}{2} w^{2} : 4 w^{2}

= lo g_{10} (4 w^{2})

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What is log_{10}(8)-log_{10}(2)+2log_{10}(w) ?
The solution to log_{10}(8)-log_{10}(2)+2log_{10}(w) is log_{10}(4w^2)