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Popular >

simplify log_{10}(1000x^5)

Solution

simplify

lo g_{10} (1000 x^{5})

Solution

3 + 5 lo g_{10} (x)

Solution steps

lo g_{10} (1000 x^{5})

Factor the number:

1000 = 1 0^{3}

= lo g_{10} (1 0^{3} x^{5})

Apply log rule:

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

lo g_{10} (1 0^{3} x^{5}) = lo g_{10} (1 0^{3}) + lo g_{10} (x^{5})

= lo g_{10} (1 0^{3}) + lo g_{10} (x^{5})

Apply log rule:

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

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

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

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)

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

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Frequently Asked Questions (FAQ)

What is log_{10}(1000x^5) ?
The solution to log_{10}(1000x^5) is 3+5log_{10}(x)