What is simplify-3/6 log_{10}(3/6)-3/6 log_{10}(3/6) ?

The solution to simplify-3/6 log_{10}(3/6)-3/6 log_{10}(3/6) is log_{10}(2)

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simplify-3/6 log_{10}(3/6)-3/6 log_{10}(3/6)

simplify

- \frac{3}{6} lo g_{10} (\frac{3}{6}) - \frac{3}{6} lo g_{10} (\frac{3}{6})

lo g_{10} (2)

Decimal Notation

0.30102 \dots

Solution steps

- \frac{3}{6} lo g_{10} (\frac{3}{6}) - \frac{3}{6} lo g_{10} (\frac{3}{6})

Add similar elements:

- \frac{3}{6} lo g_{10} (\frac{3}{6}) - \frac{3}{6} lo g_{10} (\frac{3}{6}) = - 2 \cdot \frac{3}{6} lo g_{10} (\frac{3}{6})

= - 2 \cdot \frac{3}{6} lo g_{10} (\frac{3}{6})

Cancel the numbers:

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

= - 2 \cdot \frac{3}{6} lo g_{10} (\frac{1}{2})

\frac{1}{2} = 2^{- 1}

= - 2 \cdot \frac{3}{6} lo g_{10} (2^{- 1})

Apply log rule:

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

lo g_{10} (2^{- 1}) = - 1 \cdot lo g_{10} (2)

= - 2 \cdot \frac{3}{6} (- 1 \cdot lo g_{10} (2))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{10} (2) = - lo g_{10} (2)

= - 2 \cdot \frac{3}{6} (- lo g_{10} (2))

Cancel the numbers:

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

= - 2 \cdot \frac{1}{2} (- lo g_{10} (2))

Convert

2

to fraction

: \frac{2}{1}

= - \frac{2}{1} \cdot \frac{1}{2} (- lo g_{10} (2))

Cross-cancel common factor:

2

= - 1 \cdot (- lo g_{10} (2))

Apply rule:

- a (- b) = ab

- 1 \cdot (- lo g_{10} (2)) = 1 \cdot lo g_{10} (2)

= 1 \cdot lo g_{10} (2)

Apply rule:

1 \cdot a = a

= lo g_{10} (2)

ln (\frac{e ^{2}}{9})

lo g_{10} (3 x) - lo g_{10} (x)

ln (x e^{b x})

ln (\frac{20}{7})

ln (\frac{5}{- 1})

What is simplify-3/6 log_{10}(3/6)-3/6 log_{10}(3/6) ?
The solution to simplify-3/6 log_{10}(3/6)-3/6 log_{10}(3/6) is log_{10}(2)