What is log_{10}(x^5)+3log_{10}(x^4) ?

The solution to log_{10}(x^5)+3log_{10}(x^4) is 17log_{10}(x)

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simplify log_{10}(x^5)+3log_{10}(x^4)

simplify

lo g_{10} (x^{5}) + 3 lo g_{10} (x^{4})

17 lo g_{10} (x)

Solution steps

lo g_{10} (x^{5}) + 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^{5}) = 5 lo g_{10} (x)

= 5 lo g_{10} (x) + 3 lo g_{10} (x^{4})

Simplify

3 lo g_{10} (x^{4}) : 12 lo g_{10} (x)

= 5 lo g_{10} (x) + 12 lo g_{10} (x)

Add similar elements:

5 lo g_{10} (x) + 12 lo g_{10} (x) = 17 lo g_{10} (x)

= 17 lo g_{10} (x)

ln (- 4 i)

ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{3 x}})

lo g_{10} (4 x) + lo g_{10} (x)

2 ln (x) + 3 ln (y) - ln (z)

7 ln (x) - \frac{1}{3} ln (y)

What is log_{10}(x^5)+3log_{10}(x^4) ?
The solution to log_{10}(x^5)+3log_{10}(x^4) is 17log_{10}(x)