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

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

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simplify log_{10}(x^4y^5)

simplify

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

4 lo g_{10} (x) + 5 lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{10} (y^{5}) = 5 lo g_{10} (y)

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

ln (1) + ln (15) + ln (120) + ln (680)

ln (x^{5}) - ln (x) + ln (\frac{1}{2})

lo g_{3} (x (x - 6))

- ln (5) + ln (3) + ln (\frac{3}{2})

2 ln (x - 8) - 9 ln (x)

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