What is log_{4}(2)+log_{4}(5) ?

The solution to log_{4}(2)+log_{4}(5) is log_{4}(10)

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simplify log_{4}(2)+log_{4}(5)

simplify

lo g_{4} (2) + lo g_{4} (5)

lo g_{4} (10)

Decimal Notation

1.66096 \dots

Solution steps

lo g_{4} (2) + lo g_{4} (5)

Apply log rule:

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

lo g_{4} (2) + lo g_{4} (5) = lo g_{4} (2 \cdot 5)

= lo g_{4} (2 \cdot 5)

Multiply the numbers:

2 \cdot 5 = 10

= lo g_{4} (10)

lo g_{10} (x y)

ln (\frac{1}{10})

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

3 lo g_{6} (x) + 5 lo g_{6} (x - 6)

ln (\frac{π}{2})

What is log_{4}(2)+log_{4}(5) ?
The solution to log_{4}(2)+log_{4}(5) is log_{4}(10)