What is 2log_{3}(4)-4log_{3}(5) ?

The solution to 2log_{3}(4)-4log_{3}(5) is log_{3}(16/625)

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simplify 2log_{3}(4)-4log_{3}(5)

simplify

2 lo g_{3} (4) - 4 lo g_{3} (5)

lo g_{3} (\frac{16}{625})

Decimal Notation

- 3.33617 \dots

Solution steps

2 lo g_{3} (4) - 4 lo g_{3} (5)

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

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

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

Apply log rule:

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

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

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

\frac{4 ^{2}}{5 ^{4}} = \frac{16}{625}

= lo g_{3} (\frac{16}{625})

- 3 (2 x - 5)

\frac{2}{3} \cdot \frac{1}{7}

(x - y)^{4} - 4 (x - y)^{2}

\frac{3.9 9 ^{2} - 16}{3.99 - 4}

What is 2log_{3}(4)-4log_{3}(5) ?
The solution to 2log_{3}(4)-4log_{3}(5) is log_{3}(16/625)