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

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

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

simplify

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

lo g_{5} (3 x^{2})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{v} (v^{3}) + lo g_{v} (v^{6})

lo g_{\frac{1}{2}} (\frac{3}{10})

4 lo g_{b} (x + 3) - 2 lo g_{b} (x + 2) + lo g_{b} (x)

\frac{1}{3} [2 ln (x + 3) + ln (x) + ln (x^{2} - 1)]

3.8 + lo g_{10} (\frac{0.19}{0.41})

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