What is log_{3}(4)+2log_{3}(5) ?

The solution to log_{3}(4)+2log_{3}(5) is 2log_{3}(10)

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simplify log_{3}(4)+2log_{3}(5)

simplify

lo g_{3} (4) + 2 lo g_{3} (5)

2 lo g_{3} (10)

Decimal Notation

4.19180 \dots

Solution steps

lo g_{3} (4) + 2 lo g_{3} (5)

Apply log rule:

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

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

= lo g_{3} (4) + lo g_{3} (5^{2})

Apply log rule:

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

lo g_{3} (4) + lo g_{3} (5^{2}) = lo g_{3} (4 \cdot 5^{2})

= lo g_{3} (4 \cdot 5^{2})

4 \cdot 5^{2} = 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)

6 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

ln (y) - ln (x)

lo g_{10} (a) - lo g_{10} (b) - lo g_{10} (c)

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

lo g_{10} (4) + lo g_{10} (6) - lo g_{10} (2)

What is log_{3}(4)+2log_{3}(5) ?
The solution to log_{3}(4)+2log_{3}(5) is 2log_{3}(10)