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

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

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simplify 2log_{10}(2x)

simplify

2 lo g_{10} (2 x)

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

Solution steps

2 lo g_{10} (2 x)

Apply log rule:

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

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

ln (x yz)

lo g_{\frac{3}{2}} (x) + lo g_{x} (\frac{2}{3})

lo g_{4} (\frac{g}{64})

ln (- 3) - ln (- 1)

2 lo g_{3} (3 x - 5) - lo g_{3} (1 - 6 x)

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