What is log_{3}(405)+log_{3}(5) ?

The solution to log_{3}(405)+log_{3}(5) is 2log_{3}(45)

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simplify log_{3}(405)+log_{3}(5)

simplify

lo g_{3} (405) + lo g_{3} (5)

2 lo g_{3} (45)

Decimal Notation

6.92994 \dots

Solution steps

lo g_{3} (405) + lo g_{3} (5)

Apply log rule:

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

lo g_{3} (405) + lo g_{3} (5) = lo g_{3} (405 \cdot 5)

= lo g_{3} (405 \cdot 5)

Multiply the numbers:

405 \cdot 5 = 2025

= lo g_{3} (2025)

Factor the number:

2025 = 4 5^{2}

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

Apply log rule:

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

lo g_{3} (4 5^{2}) = 2 lo g_{3} (45)

= 2 lo g_{3} (45)

ln (\frac{1}{2} e^{x})

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

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

ln (9 x^{2})

ln (\frac{e ^{- (x - θ)}}{( 1 + e ^{- (x - θ)} ) ^{2}})

What is log_{3}(405)+log_{3}(5) ?
The solution to log_{3}(405)+log_{3}(5) is 2log_{3}(45)