What is expand log_{10}(10x^3y) ?

The solution to expand log_{10}(10x^3y) is 1+3log_{10}(x)+log_{10}(y)

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expand log_{10}(10x^3y)

expand

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

1 + 3 lo g_{10} (x) + lo g_{10} (y)

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{a} (a) = 1

= 1 + 3 lo g_{10} (x) + lo g_{10} (y)

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) + C

- 0.03 \cdot ln (\frac{( 1 - 4.1 )}{82})

lo g_{10} (4 θ^{4} (1 - θ)^{4} (1 - 2 θ)^{2})

ln (x (x + 6))

ln (\frac{3}{2}) + ln (\frac{1}{2})

What is expand log_{10}(10x^3y) ?
The solution to expand log_{10}(10x^3y) is 1+3log_{10}(x)+log_{10}(y)