What is log_{6}(18x) ?

The solution to log_{6}(18x) is 1+log_{6}(3)+log_{6}(x)

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simplify log_{6}(18x)

simplify

lo g_{6} (18 x)

1 + lo g_{6} (3) + lo g_{6} (x)

Solution steps

lo g_{6} (18 x)

Factor the number:

18 = 6 \cdot 3

= lo g_{6} (6 \cdot 3 x)

Apply log rule:

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

lo g_{6} (6 \cdot 3 x) = lo g_{6} (6) + lo g_{6} (3 x)

= lo g_{6} (6) + lo g_{6} (3 x)

Apply log rule:

lo g_{a} (a) = 1

lo g_{6} (6) = 1

= 1 + lo g_{6} (3 x)

Apply log rule:

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

lo g_{6} (3 x) = lo g_{6} (3) + lo g_{6} (x)

= 1 + (lo g_{6} (3) + lo g_{6} (x))

Apply rule:

a + (b + c) = a + b + c

1 + (lo g_{6} (3) + lo g_{6} (x)) = 1 + lo g_{6} (3) + lo g_{6} (x)

= 1 + lo g_{6} (3) + lo g_{6} (x)

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