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Popular >

simplify 2log_{6}(2)+log_{6}(9)

Solution

simplify

2 lo g_{6} (2) + lo g_{6} (9)

Solution

2

Solution steps

2 lo g_{6} (2) + lo g_{6} (9)

Apply log rule:

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

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

= lo g_{6} (2^{2}) + lo g_{6} (9)

Apply log rule:

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

lo g_{6} (2^{2}) + lo g_{6} (9) = lo g_{6} (2^{2} \cdot 9)

= lo g_{6} (2^{2} \cdot 9)

2^{2} \cdot 9 = 36

= lo g_{6} (36)

Factor the number:

36 = 6^{2}

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

Apply log rule:

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

= 2

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Frequently Asked Questions (FAQ)

What is 2log_{6}(2)+log_{6}(9) ?
The solution to 2log_{6}(2)+log_{6}(9) is 2