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

The solution to log_{10}(x^2)+log_{10}(x^3) is 5log_{10}(x)

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

simplify

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

5 lo g_{10} (x)

Solution steps

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

Apply log rule

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

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

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

Apply log rule

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

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

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

Add similar elements:

2 lo g_{10} (x) + 3 lo g_{10} (x) = 5 lo g_{10} (x)

= 5 lo g_{10} (x)

\frac{1}{3} lo g_{10} (3)

lo g_{10} (z^{3} y)

ln (a) - ln (b) + ln (c)

lo g_{8} (\frac{x ^{4}}{y})

lo g_{4} (\frac{a ^{9}}{b})

What is log_{10}(x^2)+log_{10}(x^3) ?
The solution to log_{10}(x^2)+log_{10}(x^3) is 5log_{10}(x)