What is 3log_{b}(x)+log_{b}(2x+1) ?

The solution to 3log_{b}(x)+log_{b}(2x+1) is log_{b}(x^3(2x+1))

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simplify 3log_{b}(x)+log_{b}(2x+1)

simplify

3 lo g_{b} (x) + lo g_{b} (2 x + 1)

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

Solution steps

3 lo g_{b} (x) + lo g_{b} (2 x + 1)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{b} (x) = lo g_{b} (x^{3})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

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

lo g_{10} (\frac{x ^{3}}{y ^{2}})

lo g_{10} (3 x + 4) - lo g_{10} (x)

3 ln (x) - 2 ln (y)

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

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