What is 2/3 log_{b}(27)+2log_{b}(2)-log_{b}(3) ?

The solution to 2/3 log_{b}(27)+2log_{b}(2)-log_{b}(3) is log_{b}(12)

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simplify 2/3 log_{b}(27)+2log_{b}(2)-log_{b}(3)

simplify

\frac{2}{3} lo g_{b} (27) + 2 lo g_{b} (2) - lo g_{b} (3)

lo g_{b} (12)

Solution steps

\frac{2}{3} lo g_{b} (27) + 2 lo g_{b} (2) - lo g_{b} (3)

Simplify

\frac{2}{3} lo g_{b} (27) : 2 lo g_{b} (3)

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

Group like terms

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

Add similar elements:

2 lo g_{b} (3) - lo g_{b} (3) = lo g_{b} (3)

= lo g_{b} (3) + 2 lo g_{b} (2)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{b} (2) = lo g_{b} (2^{2})

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

Apply log rule:

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

lo g_{b} (3) + lo g_{b} (2^{2}) = lo g_{b} (3 \cdot 2^{2})

= lo g_{b} (3 \cdot 2^{2})

3 \cdot 2^{2} = 12

= lo g_{b} (12)

- \frac{8}{12} lo g_{2} (\frac{8}{12}) - \frac{4}{12} lo g_{2} (\frac{4}{12})

ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1

lo g_{10} (12 x) - lo g_{10} (3 x)

ln (4 h - 8) - ln (4)

\frac{1}{2} ln (x) + 6 ln (y) - 5 ln (z)

What is 2/3 log_{b}(27)+2log_{b}(2)-log_{b}(3) ?
The solution to 2/3 log_{b}(27)+2log_{b}(2)-log_{b}(3) is log_{b}(12)