What is 2log_{7}(3x)+3log_{7}(2x) ?

The solution to 2log_{7}(3x)+3log_{7}(2x) is log_{7}(72x^5)

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simplify 2log_{7}(3x)+3log_{7}(2x)

simplify

2 lo g_{7} (3 x) + 3 lo g_{7} (2 x)

lo g_{7} (72 x^{5})

Solution steps

2 lo g_{7} (3 x) + 3 lo g_{7} (2 x)

2 lo g_{7} (3 x) = lo g_{7} ((3 x)^{2})

3 lo g_{7} (2 x) = lo g_{7} ((2 x)^{3})

= lo g_{7} ((3 x)^{2}) + lo g_{7} ((2 x)^{3})

Apply log rule:

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

lo g_{7} ((3 x)^{2}) + lo g_{7} ((2 x)^{3}) = lo g_{7} ((3 x)^{2} (2 x)^{3})

= lo g_{7} ((3 x)^{2} (2 x)^{3})

Simplify

(3 x)^{2} (2 x)^{3} : 72 x^{5}

= lo g_{7} (72 x^{5})

lo g_{3} (\frac{27}{x + 8})

lo g_{2} (\frac{8 x ^{3}}{x ^{2} - 1})

lo g_{5} (\frac{f}{125})

lo g_{10} (10 x^{5})

ln (x x^{2} + 5)

What is 2log_{7}(3x)+3log_{7}(2x) ?
The solution to 2log_{7}(3x)+3log_{7}(2x) is log_{7}(72x^5)