What is log_{10}(5)+2log_{10}(x)+log_{10}(3) ?

The solution to log_{10}(5)+2log_{10}(x)+log_{10}(3) is log_{10}(15x^2)

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simplify log_{10}(5)+2log_{10}(x)+log_{10}(3)

simplify

lo g_{10} (5) + 2 lo g_{10} (x) + lo g_{10} (3)

lo g_{10} (15 x^{2})

Solution steps

lo g_{10} (5) + 2 lo g_{10} (x) + lo g_{10} (3)

Apply log rule:

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

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

= lo g_{10} (5) + lo g_{10} (x^{2}) + lo g_{10} (3)

Apply log rule:

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

lo g_{10} (5) + lo g_{10} (x^{2}) = lo g_{10} (5 x^{2})

= lo g_{10} (5 x^{2}) + lo g_{10} (3)

Apply log rule:

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

lo g_{10} (5 x^{2}) + lo g_{10} (3) = lo g_{10} (5 x^{2} \cdot 3)

= lo g_{10} (5 x^{2} \cdot 3)

Simplify

5 x^{2} \cdot 3 : 15 x^{2}

= lo g_{10} (15 x^{2})

ln (\frac{1}{x})

lo g_{10} (\frac{10 x}{6})

lo g_{b} (60) + lo g_{b} (3)

ln (p) - ln (p - 6500)

\frac{1}{4} lo g_{10} (a) - \frac{1}{5} lo g_{10} (b)

What is log_{10}(5)+2log_{10}(x)+log_{10}(3) ?
The solution to log_{10}(5)+2log_{10}(x)+log_{10}(3) is log_{10}(15x^2)