What is log_{5}(5/7)+log_{5}(49/25) ?

The solution to log_{5}(5/7)+log_{5}(49/25) is log_{5}(7/5)

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simplify log_{5}(5/7)+log_{5}(49/25)

simplify

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

lo g_{5} (\frac{7}{5})

Decimal Notation

0.20906 \dots

Solution steps

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

Apply log rule:

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

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25}) = lo g_{5} (\frac{5}{7} \cdot \frac{49}{25})

= lo g_{5} (\frac{5}{7} \cdot \frac{49}{25})

\frac{5}{7} \cdot \frac{49}{25} = \frac{7}{5}

= lo g_{5} (\frac{7}{5})

lo g_{4} (\frac{7}{19}) + lo g_{4} (\frac{19}{7})

7 lo g_{6} (x - 2) + 2 lo g_{6} (3 x)

lo g_{10} (0.0001) - lo g_{10} (0.1)

4 lo g_{10} (x) + 3 lo g_{10} (y)

ln (\frac{( d - r ) ^{2}}{r ^{2}})

What is log_{5}(5/7)+log_{5}(49/25) ?
The solution to log_{5}(5/7)+log_{5}(49/25) is log_{5}(7/5)