What is log_{10}(x^2sqrt(x^3+1)) ?

The solution to log_{10}(x^2sqrt(x^3+1)) is 2log_{10}(x)+log_{10}(sqrt(x^3+1))

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simplify log_{10}(x^2sqrt(x^3+1))

simplify

lo g_{10} (x^{2} x^{3} + 1)

2 lo g_{10} (x) + lo g_{10} (x^{3} + 1)

Solution steps

lo g_{10} (x^{2} x^{3} + 1)

Apply log rule:

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

lo g_{10} (x^{2} x^{3} + 1) = lo g_{10} (x^{2}) + lo g_{10} (x^{3} + 1)

= lo g_{10} (x^{2}) + lo g_{10} (x^{3} + 1)

Simplify

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

= 2 lo g_{10} (x) + lo g_{10} (x^{3} + 1)

4 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{7} ((5) (c))

3 \cdot ln (pq) + 4 \cdot ln (p q^{2})

\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})

lo g_{4} (2) + 2 lo g_{4} (9)

What is log_{10}(x^2sqrt(x^3+1)) ?
The solution to log_{10}(x^2sqrt(x^3+1)) is 2log_{10}(x)+log_{10}(sqrt(x^3+1))