What is log_{5}(6/27)+log_{5}(3/2) ?

The solution to log_{5}(6/27)+log_{5}(3/2) is -log_{5}(3)

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simplify log_{5}(6/27)+log_{5}(3/2)

simplify

lo g_{5} (\frac{6}{27}) + lo g_{5} (\frac{3}{2})

- lo g_{5} (3)

Decimal Notation

- 0.68260 \dots

Solution steps

lo g_{5} (\frac{6}{27}) + lo g_{5} (\frac{3}{2})

Apply log rule:

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

lo g_{5} (\frac{6}{27}) + lo g_{5} (\frac{3}{2}) = lo g_{5} (\frac{6}{27} \cdot \frac{3}{2})

= lo g_{5} (\frac{6}{27} \cdot \frac{3}{2})

\frac{6}{27} \cdot \frac{3}{2} = \frac{1}{3}

= lo g_{5} (\frac{1}{3})

\frac{1}{3} = 3^{- 1}

= lo g_{5} (3^{- 1})

Apply log rule:

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

lo g_{5} (3^{- 1}) = - 1 \cdot lo g_{5} (3)

= - 1 \cdot lo g_{5} (3)

Apply rule:

1 \cdot a = a

= - lo g_{5} (3)

lo g_{5} (\frac{z}{125})

lo g_{10} (\frac{7 x}{13})

\frac{2 ln ( 3 ) + 2 ln ( 5 )}{4}

lo g_{6} (36 x^{3})

lo g_{10} (x^{\frac{1}{2}} y^{\frac{1}{3}})

What is log_{5}(6/27)+log_{5}(3/2) ?
The solution to log_{5}(6/27)+log_{5}(3/2) is -log_{5}(3)