What is 2log_{3}(5)-log_{3}(14)+log_{9}(3) ?

The solution to 2log_{3}(5)-log_{3}(14)+log_{9}(3) is log_{3}(25/14)+1/2

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simplify 2log_{3}(5)-log_{3}(14)+log_{9}(3)

simplify

2 lo g_{3} (5) - lo g_{3} (14) + lo g_{9} (3)

lo g_{3} (\frac{25}{14}) + \frac{1}{2}

Decimal Notation

1.02777 \dots

Solution steps

2 lo g_{3} (5) - lo g_{3} (14) + lo g_{9} (3)

lo g_{9} (3) = \frac{1}{2}

= 2 lo g_{3} (5) - lo g_{3} (14) + \frac{1}{2}

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} (5^{2}) - lo g_{3} (14) + \frac{1}{2}

lo g_{3} (5^{2}) - lo g_{3} (14) = lo g_{3} (\frac{25}{14})

= lo g_{3} (\frac{25}{14}) + \frac{1}{2}

lo g_{10} (18) + lo g_{10} (8) - 2 lo g_{10} (25)

lo g_{10} (p) + 2 lo g_{10} (8 s)

ln (x (x - 1))

ln (\frac{3 ^{x} 6 ^{2 x}}{2 ^{3 x}})

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

What is 2log_{3}(5)-log_{3}(14)+log_{9}(3) ?
The solution to 2log_{3}(5)-log_{3}(14)+log_{9}(3) is log_{3}(25/14)+1/2