What is log_{6}(4)+log_{6}(54) ?

The solution to log_{6}(4)+log_{6}(54) is 3

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simplify log_{6}(4)+log_{6}(54)

simplify

lo g_{6} (4) + lo g_{6} (54)

3

Solution steps

lo g_{6} (4) + lo g_{6} (54)

Apply log rule:

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

lo g_{6} (4) + lo g_{6} (54) = lo g_{6} (4 \cdot 54)

= lo g_{6} (4 \cdot 54)

Multiply the numbers:

4 \cdot 54 = 216

= lo g_{6} (216)

Factor the number:

216 = 6^{3}

= lo g_{6} (6^{3})

Apply log rule:

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

= 3

(\frac{3 x y}{z ^{- 2}})^{3}

\frac{115}{2}

(x + 9) (x - 8)

lo g_{10} (2.6)

- 12 - (- 7)