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

The solution to 2log_{10}(y^3)+log_{10}(y^2) is 8log_{10}(y)

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

simplify

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

8 lo g_{10} (y)

Solution steps

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

Simplify

2 lo g_{10} (y^{3}) : 6 lo g_{10} (y)

= 6 lo g_{10} (y) + lo g_{10} (y^{2})

Apply log rule

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

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

= 6 lo g_{10} (y) + 2 lo g_{10} (y)

Add similar elements:

6 lo g_{10} (y) + 2 lo g_{10} (y) = 8 lo g_{10} (y)

= 8 lo g_{10} (y)

lo g_{a} (x^{2}) - 2 lo g_{a} (x)

4 lo g_{3} (x^{2} - 1) - 2 lo g_{3} (x + 1)

lo g_{3} (7 \cdot 5)

ln (y e^{- x})

6 lo g_{2} (22) + 1460 - 6 lo g_{2} (24) + 2002

What is 2log_{10}(y^3)+log_{10}(y^2) ?
The solution to 2log_{10}(y^3)+log_{10}(y^2) is 8log_{10}(y)