What is 2log_{3}(6)-log_{3}(8) ?

The solution to 2log_{3}(6)-log_{3}(8) is log_{3}(9/2)

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simplify 2log_{3}(6)-log_{3}(8)

simplify

2 lo g_{3} (6) - lo g_{3} (8)

lo g_{3} (\frac{9}{2})

Decimal Notation

1.36907 \dots

Solution steps

2 lo g_{3} (6) - lo g_{3} (8)

Apply log rule:

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

2 lo g_{3} (6) = lo g_{3} (6^{2})

= lo g_{3} (6^{2}) - lo g_{3} (8)

Apply log rule:

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

lo g_{3} (6^{2}) - lo g_{3} (8) = lo g_{3} (\frac{6 ^{2}}{8})

= lo g_{3} (\frac{6 ^{2}}{8})

\frac{6 ^{2}}{8} = \frac{9}{2}

= lo g_{3} (\frac{9}{2})

lo g_{4} (\frac{x ^{2}}{y ^{6}})

lo g_{a} (\frac{1}{64})

- lo g_{10} (5 \cdot 1 0^{- 6})

lo g_{b} (125 k)

What is 2log_{3}(6)-log_{3}(8) ?
The solution to 2log_{3}(6)-log_{3}(8) is log_{3}(9/2)