What is log_{5}(4)+log_{5}(9) ?

The solution to log_{5}(4)+log_{5}(9) is 2log_{5}(6)

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simplify log_{5}(4)+log_{5}(9)

simplify

lo g_{5} (4) + lo g_{5} (9)

2 lo g_{5} (6)

Decimal Notation

2.22656 \dots

Solution steps

lo g_{5} (4) + lo g_{5} (9)

Apply log rule:

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

lo g_{5} (4) + lo g_{5} (9) = lo g_{5} (4 \cdot 9)

= lo g_{5} (4 \cdot 9)

Multiply the numbers:

4 \cdot 9 = 36

= lo g_{5} (36)

Factor the number:

36 = 6^{2}

= lo g_{5} (6^{2})

Apply log rule:

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

lo g_{5} (6^{2}) = 2 lo g_{5} (6)

= 2 lo g_{5} (6)

\frac{1}{5800} ln (\frac{1}{2})

3 lo g_{10} (4) + 2 lo g_{10} (x)

ln (\frac{x}{y ^{5} z})

3 lo g_{10} (2) + 2 lo g_{10} (5)

ln (3.61 \cdot 1 0^{- 11})

What is log_{5}(4)+log_{5}(9) ?
The solution to log_{5}(4)+log_{5}(9) is 2log_{5}(6)