What is 4log_{10}(x)+log_{10}(x^2)-log_{10}(x^4) ?

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

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simplify 4log_{10}(x)+log_{10}(x^2)-log_{10}(x^4)

simplify

4 lo g_{10} (x) + lo g_{10} (x^{2}) - lo g_{10} (x^{4})

lo g_{10} (x^{2})

Solution steps

4 lo g_{10} (x) + lo g_{10} (x^{2}) - lo g_{10} (x^{4})

Apply log rule:

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

4 lo g_{10} (x) = lo g_{10} (x^{4})

= lo g_{10} (x^{4}) + lo g_{10} (x^{2}) - lo g_{10} (x^{4})

Apply log rule:

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

lo g_{10} (x^{4}) + lo g_{10} (x^{2}) = lo g_{10} (x^{4} x^{2})

= lo g_{10} (x^{4} x^{2}) - lo g_{10} (x^{4})

Simplify

x^{4} x^{2} : x^{6}

= lo g_{10} (x^{6}) - lo g_{10} (x^{4})

Apply log rule:

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

lo g_{10} (x^{6}) - lo g_{10} (x^{4}) = lo g_{10} (\frac{x ^{6}}{x ^{4}})

= lo g_{10} (\frac{x ^{6}}{x ^{4}})

Simplify

\frac{x ^{6}}{x ^{4}} : x^{2}

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

lo g_{9} (\frac{2 x ^{3}}{3})

\frac{1}{2} lo g_{a} (x) - 8 lo g_{a} (y) + lo g_{a} (z)

ln (42)

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

lo g_{2} (\frac{x ^{2} x + 1}{x ^{3}})

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