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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{\frac{1}{2}} (\frac{3 x ^{2}}{2})

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

2 ln (3) - ln (2)

2 ln (3) - ln (5)

2 lo g_{10} (3 x) - lo g_{10} (7 x)

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