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

The solution to 5log_{10}(3)+2log_{10}(x) is log_{10}(243x^2)

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

simplify

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

lo g_{10} (243 x^{2})

Solution steps

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

5 lo g_{10} (3) = lo g_{10} (3^{5})

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

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

Apply log rule:

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

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

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

Simplify

3^{5} x^{2} : 243 x^{2}

= lo g_{10} (243 x^{2})

ln (\frac{400}{369})

5 ln (x - 2) - ln (x + 2) - 3 ln (x)

ln (e^{i 0}) - ln (3 e^{i 0} + 4)

12 ln (x) - 14 ln (\frac{1}{y}) - 13 ln (x y)

lo g_{c} (m) + lo g_{c} (n)

What is 5log_{10}(3)+2log_{10}(x) ?
The solution to 5log_{10}(3)+2log_{10}(x) is log_{10}(243x^2)