What is log_{5}(7)+log_{5}(3) ?

The solution to log_{5}(7)+log_{5}(3) is log_{5}(21)

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simplify log_{5}(7)+log_{5}(3)

simplify

lo g_{5} (7) + lo g_{5} (3)

lo g_{5} (21)

Decimal Notation

1.89166 \dots

Solution steps

lo g_{5} (7) + lo g_{5} (3)

Apply log rule:

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

lo g_{5} (7) + lo g_{5} (3) = lo g_{5} (7 \cdot 3)

= lo g_{5} (7 \cdot 3)

Multiply the numbers:

7 \cdot 3 = 21

= lo g_{5} (21)

\frac{1}{7} (lo g_{10} (x) - lo g_{10} (x + 4))

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

ln (x^{5} (1 - x)^{3})

- \frac{8}{9} lo g_{2} (\frac{8}{9}) - \frac{1}{9} lo g_{2} (\frac{1}{9})

\frac{1}{2} lo g_{b} (x) + 3 lo g_{b} (y) - 2 lo g_{b} (x)

What is log_{5}(7)+log_{5}(3) ?
The solution to log_{5}(7)+log_{5}(3) is log_{5}(21)