What is 1/3 log_{3}(8)+log_{3}(6)-log_{3}(3) ?

The solution to 1/3 log_{3}(8)+log_{3}(6)-log_{3}(3) is 2log_{3}(2)

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simplify 1/3 log_{3}(8)+log_{3}(6)-log_{3}(3)

simplify

\frac{1}{3} lo g_{3} (8) + lo g_{3} (6) - lo g_{3} (3)

2 lo g_{3} (2)

Decimal Notation

1.26185 \dots

Solution steps

\frac{1}{3} lo g_{3} (8) + lo g_{3} (6) - lo g_{3} (3)

Apply log rule:

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

\frac{1}{3} lo g_{3} (8) = lo g_{3} (8^{\frac{1}{3}})

= lo g_{3} (8^{\frac{1}{3}}) + lo g_{3} (6) - lo g_{3} (3)

Apply log rule:

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

lo g_{3} (8^{\frac{1}{3}}) + lo g_{3} (6) = lo g_{3} (8^{\frac{1}{3}} \cdot 6)

= lo g_{3} (8^{\frac{1}{3}} \cdot 6) - lo g_{3} (3)

Apply log rule:

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

lo g_{3} (8^{\frac{1}{3}} \cdot 6) - lo g_{3} (3) = lo g_{3} (\frac{8 ^{\frac{1}{3}} \cdot 6}{3})

= lo g_{3} (\frac{8 ^{\frac{1}{3}} \cdot 6}{3})

Cancel

\frac{8 ^{\frac{1}{3}} \cdot 6}{3} : 4

= lo g_{3} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{3} (2)

lo g_{3} (81 x^{3} 1 + x^{2})

- lo g_{10} (4.35 \cdot 1 0^{- 6})

ln (\frac{( 70 - 95 )}{( 5 - 95 ) ( 1.9958 )})

ln (23) - ln (7)

What is 1/3 log_{3}(8)+log_{3}(6)-log_{3}(3) ?
The solution to 1/3 log_{3}(8)+log_{3}(6)-log_{3}(3) is 2log_{3}(2)