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Popular >

simplify log_{10}(100x^3)

Solution

simplify

lo g_{10} (100 x^{3})

Solution

2 + 3 lo g_{10} (x)

Solution steps

lo g_{10} (100 x^{3})

Factor the number:

100 = 1 0^{2}

= lo g_{10} (1 0^{2} x^{3})

Apply log rule:

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

lo g_{10} (1 0^{2} x^{3}) = lo g_{10} (1 0^{2}) + lo g_{10} (x^{3})

= lo g_{10} (1 0^{2}) + lo g_{10} (x^{3})

Apply log rule:

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

lo g_{10} (1 0^{2}) = 2

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

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

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Frequently Asked Questions (FAQ)

What is log_{10}(100x^3) ?
The solution to log_{10}(100x^3) is 2+3log_{10}(x)