What is log_{10}(4)+3log_{10}(x)+log_{10}(y) ?

The solution to log_{10}(4)+3log_{10}(x)+log_{10}(y) is log_{10}(4x^3y)

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simplify log_{10}(4)+3log_{10}(x)+log_{10}(y)

simplify

lo g_{10} (4) + 3 lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (4 x^{3} y)

Solution steps

lo g_{10} (4) + 3 lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (4) = 2 lo g_{10} (2)

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

2^{2} x^{3} y : 4 x^{3} y

= lo g_{10} (4 x^{3} y)

8 ln (x) - \frac{1}{4} ln (y)

lo g_{8} (c) + 4 lo g_{8} (a) - 5 lo g_{8} (b)

lo g_{4} (7^{2} 3^{4})

ln (2 x y)

lo g_{2} (x + 1) - lo g_{2} (2 - x)

What is log_{10}(4)+3log_{10}(x)+log_{10}(y) ?
The solution to log_{10}(4)+3log_{10}(x)+log_{10}(y) is log_{10}(4x^3y)