What is log_{3}(3x+4)-7log_{9}(x^2)+6log_{3}(x) ?

The solution to log_{3}(3x+4)-7log_{9}(x^2)+6log_{3}(x) is log_{3}((3x+4)/x)

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simplify log_{3}(3x+4)-7log_{9}(x^2)+6log_{3}(x)

simplify

lo g_{3} (3 x + 4) - 7 lo g_{9} (x^{2}) + 6 lo g_{3} (x)

lo g_{3} (\frac{3 x + 4}{x})

Solution steps

lo g_{3} (3 x + 4) - 7 lo g_{9} (x^{2}) + 6 lo g_{3} (x)

Simplify

lo g_{9} (x^{2}) : lo g_{3} (x)

= lo g_{3} (3 x + 4) - 7 lo g_{3} (x) + 6 lo g_{3} (x)

Add similar elements:

- 7 lo g_{3} (x) + 6 lo g_{3} (x) = - lo g_{3} (x)

= lo g_{3} (3 x + 4) - lo g_{3} (x)

Apply log rule:

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

lo g_{3} (3 x + 4) - lo g_{3} (x) = lo g_{3} (\frac{3 x + 4}{x})

= lo g_{3} (\frac{3 x + 4}{x})

lo g_{7} (5) - lo g_{7} (2)

\frac{3}{4} ln (3)

lo g_{10} (2 y^{2})

lo g_{9} (4 n p^{3})

What is log_{3}(3x+4)-7log_{9}(x^2)+6log_{3}(x) ?
The solution to log_{3}(3x+4)-7log_{9}(x^2)+6log_{3}(x) is log_{3}((3x+4)/x)