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Popular >

simplify log_{6}(36x^7)

Solution

simplify

lo g_{6} (36 x^{7})

Solution

2 + 7 lo g_{6} (x)

Solution steps

lo g_{6} (36 x^{7})

Factor the number:

36 = 6^{2}

= lo g_{6} (6^{2} x^{7})

Apply log rule:

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

lo g_{6} (6^{2} x^{7}) = lo g_{6} (6^{2}) + lo g_{6} (x^{7})

= lo g_{6} (6^{2}) + lo g_{6} (x^{7})

Apply log rule:

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

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

= 2 + lo g_{6} (x^{7})

Apply log rule

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

lo g_{6} (x^{7}) = 7 lo g_{6} (x)

= 2 + 7 lo g_{6} (x)

Popular Examples

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Frequently Asked Questions (FAQ)

What is log_{6}(36x^7) ?
The solution to log_{6}(36x^7) is 2+7log_{6}(x)