What is log_{3}(8)+log_{3}(4) ?

The solution to log_{3}(8)+log_{3}(4) is 5log_{3}(2)

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simplify log_{3}(8)+log_{3}(4)

simplify

lo g_{3} (8) + lo g_{3} (4)

5 lo g_{3} (2)

Decimal Notation

3.15464 \dots

Solution steps

lo g_{3} (8) + lo g_{3} (4)

Apply log rule:

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

lo g_{3} (8) + lo g_{3} (4) = lo g_{3} (8 \cdot 4)

= lo g_{3} (8 \cdot 4)

Multiply the numbers:

8 \cdot 4 = 32

= lo g_{3} (32)

Factor the number:

32 = 2^{5}

= lo g_{3} (2^{5})

Apply log rule:

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

lo g_{3} (2^{5}) = 5 lo g_{3} (2)

= 5 lo g_{3} (2)

- \frac{3}{5} \cdot lo g_{2} (\frac{3}{5}) - \frac{2}{5} \cdot lo g_{2} (\frac{2}{5})

lo g_{10} (\frac{x ^{9}}{y ^{4}})

lo g_{10} (\frac{x}{y})

ln (\frac{25}{9})

lo g_{3} (\frac{9}{x + 5})

What is log_{3}(8)+log_{3}(4) ?
The solution to log_{3}(8)+log_{3}(4) is 5log_{3}(2)