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

The solution to 2log_{3}(5)-log_{3}(2) is log_{3}(25/2)

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simplify 2log_{3}(5)-log_{3}(2)

simplify

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

lo g_{3} (\frac{25}{2})

Decimal Notation

2.29901 \dots

Solution steps

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

5^{2} = 25

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

ln (\frac{x ^{8} p ^{7} q ^{9}}{e ^{9}})

- 2 ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ + ln x^{2} + 1 + C

- lo g_{10} (a) + 2 lo g_{10} (b) - 1

lo g_{10} (\frac{x ^{2}}{( x - 5 ) ^{2}})

ln (\frac{( 1 + x )}{( 1 - x )})

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