What is 3log_{10}(x*x^3) ?

The solution to 3log_{10}(x*x^3) is 12log_{10}(x)

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simplify 3log_{10}(x*x^3)

simplify

3 lo g_{10} (x \cdot x^{3})

12 lo g_{10} (x)

Solution steps

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

Simplify

x x^{3} : x^{4}

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

Apply log rule

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

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

= 3 \cdot 4 lo g_{10} (x)

Multiply the numbers:

3 \cdot 4 = 12

= 12 lo g_{10} (x)

\frac{1}{2} lo g_{10} (16) - \frac{1}{3} lo g_{10} (8) + 1

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

lo g_{5} (5 x)

lo g_{10} (\frac{x ^{2}}{z y})

lo g_{10} (5 x^{4})