What is log_{6}(36x^6) ?

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

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simplify log_{6}(36x^6)

simplify

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

2 + 6 lo g_{6} (x)

Solution steps

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

Factor the number:

36 = 6^{2}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule

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

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

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

lo g_{7} (\frac{3 x ^{2}}{y ^{3}})

ln (\frac{x ^{4}}{( 2 x - 1 ) ^{3} ( 7 x - 5 ) ^{8}})

4 ln (x) - \frac{1}{3} ln (x^{2} + 1) + 2 ln (x - 1)

lo g_{10} (\frac{y ^{2}}{2 z})

lo g_{10} (18) - lo g_{10} (6)