What is log_{10}(4)+2log_{10}(x) ?

The solution to log_{10}(4)+2log_{10}(x) is log_{10}(4x^2)

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simplify log_{10}(4)+2log_{10}(x)

simplify

lo g_{10} (4) + 2 lo g_{10} (x)

lo g_{10} (4 x^{2})

Solution steps

lo g_{10} (4) + 2 lo g_{10} (x)

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

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

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

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

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

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

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

Simplify

2^{2} x^{2} : 4 x^{2}

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

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What is log_{10}(4)+2log_{10}(x) ?
The solution to log_{10}(4)+2log_{10}(x) is log_{10}(4x^2)