What is log_{2}(3x+1)-3log_{4}(x^2)+2log_{2}(x) ?

The solution to log_{2}(3x+1)-3log_{4}(x^2)+2log_{2}(x) is log_{2}((3x+1)/x)

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simplify log_{2}(3x+1)-3log_{4}(x^2)+2log_{2}(x)

simplify

lo g_{2} (3 x + 1) - 3 lo g_{4} (x^{2}) + 2 lo g_{2} (x)

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

Solution steps

lo g_{2} (3 x + 1) - 3 lo g_{4} (x^{2}) + 2 lo g_{2} (x)

Simplify

lo g_{4} (x^{2}) : lo g_{2} (x)

= lo g_{2} (3 x + 1) - 3 lo g_{2} (x) + 2 lo g_{2} (x)

Add similar elements:

- 3 lo g_{2} (x) + 2 lo g_{2} (x) = - lo g_{2} (x)

= lo g_{2} (3 x + 1) - lo g_{2} (x)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (3 x + 1) - lo g_{2} (x) = lo g_{2} (\frac{3 x + 1}{x})

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

lo g_{10} (\frac{z y ^{3}}{x})

ln (6.57 \cdot 1 0^{173})

lo g_{3} (7 y)

lo g_{n} (a) - lo g_{n} (a - n)

ln (2) + ln (4) + ln (6)

What is log_{2}(3x+1)-3log_{4}(x^2)+2log_{2}(x) ?
The solution to log_{2}(3x+1)-3log_{4}(x^2)+2log_{2}(x) is log_{2}((3x+1)/x)