What is 2log_{3}(0.5)+2log_{3}(5)-2log_{3}(5/6) ?

The solution to 2log_{3}(0.5)+2log_{3}(5)-2log_{3}(5/6) is 2

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simplify 2log_{3}(0.5)+2log_{3}(5)-2log_{3}(5/6)

simplify

2 lo g_{3} (0.5) + 2 lo g_{3} (5) - 2 lo g_{3} (\frac{5}{6})

2

Solution steps

2 lo g_{3} (0.5) + 2 lo g_{3} (5) - 2 lo g_{3} (\frac{5}{6})

2 lo g_{3} (0.5) = lo g_{3} (0. 5^{2})

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

- 2 lo g_{3} (\frac{5}{6}) = - lo g_{3} ((\frac{5}{6})^{2})

= lo g_{3} (0. 5^{2}) + lo g_{3} (5^{2}) - lo g_{3} ((\frac{5}{6})^{2})

Apply log rule:

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

lo g_{3} (0. 5^{2}) + lo g_{3} (5^{2}) = lo g_{3} (0. 5^{2} \cdot 5^{2})

= lo g_{3} (0. 5^{2} \cdot 5^{2}) - lo g_{3} ((\frac{5}{6})^{2})

Apply log rule:

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

lo g_{3} (0. 5^{2} \cdot 5^{2}) - lo g_{3} ((\frac{5}{6})^{2}) = lo g_{3} (\frac{0. 5 ^{2} \cdot 5 ^{2}}{( \frac{5}{6} ) ^{2}})

= lo g_{3} (\frac{0. 5 ^{2} \cdot 5 ^{2}}{( \frac{5}{6} ) ^{2}})

\frac{0. 5 ^{2} \cdot 5 ^{2}}{( \frac{5}{6} ) ^{2}} = 9

= lo g_{3} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

lo g_{a} (a^{b}) = b

= 2

ln (\frac{x}{( x + 2 ) ^{2}})

0.94 \cdot ln (3 \cdot 1 0^{6}) + 0.06 ln (6000)

ln (\frac{39}{51})

ln (\frac{6}{π ^{2}})

ln (\frac{5 a}{b c})

What is 2log_{3}(0.5)+2log_{3}(5)-2log_{3}(5/6) ?
The solution to 2log_{3}(0.5)+2log_{3}(5)-2log_{3}(5/6) is 2