What is log_{3}(0.0994)+log_{3}(4.5497) ?

The solution to log_{3}(0.0994)+log_{3}(4.5497) is log_{3}(22612009/50000000)

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simplify log_{3}(0.0994)+log_{3}(4.5497)

simplify

lo g_{3} (0.0994) + lo g_{3} (4.5497)

lo g_{3} (\frac{22612009}{50000000})

Decimal Notation

- 0.72231 \dots

Solution steps

lo g_{3} (0.0994) + lo g_{3} (4.5497)

Apply log rule:

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

lo g_{3} (0.0994) + lo g_{3} (4.5497) = lo g_{3} (0.0994 \cdot 4.5497)

= lo g_{3} (0.0994 \cdot 4.5497)

Multiply the numbers:

0.0994 \cdot 4.5497 = 0.45224018

= lo g_{3} (0.45224018)

0.45224018 = \frac{45224018}{100000000}

= lo g_{3} (\frac{45224018}{100000000})

Cancel

\frac{45224018}{100000000} : \frac{22612009}{50000000}

= lo g_{3} (\frac{22612009}{50000000})

lo g_{a} (8) + lo g_{a} (5) + 2 lo g_{a} (2)

lo g_{b} (m \cdot n)

6 ln (x) + 6 ln (y)

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

What is log_{3}(0.0994)+log_{3}(4.5497) ?
The solution to log_{3}(0.0994)+log_{3}(4.5497) is log_{3}(22612009/50000000)