What is log_{3}(25)+log_{3}(4) ?

The solution to log_{3}(25)+log_{3}(4) is 2log_{3}(10)

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simplify log_{3}(25)+log_{3}(4)

simplify

lo g_{3} (25) + lo g_{3} (4)

2 lo g_{3} (10)

Decimal Notation

4.19180 \dots

Solution steps

lo g_{3} (25) + lo g_{3} (4)

Apply log rule:

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

lo g_{3} (25) + lo g_{3} (4) = lo g_{3} (25 \cdot 4)

= lo g_{3} (25 \cdot 4)

Multiply the numbers:

25 \cdot 4 = 100

= lo g_{3} (100)

Factor the number:

100 = 1 0^{2}

= lo g_{3} (1 0^{2})

Apply log rule:

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

lo g_{3} (1 0^{2}) = 2 lo g_{3} (10)

= 2 lo g_{3} (10)

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

ln (- 3 y)

- lo g_{10} (3 \cdot 1 0^{- 6})

- lo g_{10} (7.5 \times 1 0^{- 6})

lo g_{e} (3 x)

What is log_{3}(25)+log_{3}(4) ?
The solution to log_{3}(25)+log_{3}(4) is 2log_{3}(10)