What is log_{10}(243/32)+log_{10}(32/243) ?

The solution to log_{10}(243/32)+log_{10}(32/243) is 0

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simplify log_{10}(243/32)+log_{10}(32/243)

simplify

lo g_{10} (\frac{243}{32}) + lo g_{10} (\frac{32}{243})

0

Solution steps

lo g_{10} (\frac{243}{32}) + lo g_{10} (\frac{32}{243})

Apply log rule:

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

lo g_{10} (\frac{243}{32}) + lo g_{10} (\frac{32}{243}) = lo g_{10} (\frac{243}{32} \cdot \frac{32}{243})

= lo g_{10} (\frac{243}{32} \cdot \frac{32}{243})

Cross cancel:

\frac{a}{b} \cdot \frac{b}{a} = 1

\frac{243}{32} \cdot \frac{32}{243} = 1

= lo g_{10} (1)

Apply log rule:

lo g_{a} (1) = 0

= 0

lo g_{10} (\frac{1}{10 x})

ln (6) - ln (5)

4 lo g_{3} (x^{2}) - 3 lo g_{3} (x^{3})

lo g_{7} (\frac{2}{3})

lo g_{5} (2) + lo g_{5} (x^{2})

What is log_{10}(243/32)+log_{10}(32/243) ?
The solution to log_{10}(243/32)+log_{10}(32/243) is 0