What is 3log_{10}(x^3)+log_{10}(x)-log_{10}(x^4) ?

The solution to 3log_{10}(x^3)+log_{10}(x)-log_{10}(x^4) is log_{10}(x^6)

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simplify 3log_{10}(x^3)+log_{10}(x)-log_{10}(x^4)

simplify

3 lo g_{10} (x^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

lo g_{10} (x^{6})

Solution steps

3 lo g_{10} (x^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

Apply log rule:

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

3 lo g_{10} (x^{3}) = lo g_{10} ((x^{3})^{3})

= lo g_{10} ((x^{3})^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

Apply log rule:

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

lo g_{10} ((x^{3})^{3}) + lo g_{10} (x) = lo g_{10} (x (x^{3})^{3})

= lo g_{10} (x (x^{3})^{3}) - lo g_{10} (x^{4})

Simplify

(x^{3})^{3} x : x^{10}

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

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

Simplify

\frac{x ^{10}}{x ^{4}} : x^{6}

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

ln (\frac{25}{20})

lo g_{b} (2) + lo g_{b} (3)

- \frac{7}{8} lo g_{2} (\frac{7}{8}) - \frac{1}{8} lo g_{2} (\frac{1}{8})

lo g_{10} (\frac{x}{z ^{5} y ^{3}})

2 lo g_{b} (x) + 4 lo g_{b} (z)

What is 3log_{10}(x^3)+log_{10}(x)-log_{10}(x^4) ?
The solution to 3log_{10}(x^3)+log_{10}(x)-log_{10}(x^4) is log_{10}(x^6)