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

The solution to 3log_{9}(2)-2log_{9}(5) is log_{9}(8/25)

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

simplify

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

lo g_{9} (\frac{8}{25})

Decimal Notation

- 0.51857 \dots

Solution steps

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

3 lo g_{9} (2) = lo g_{9} (2^{3})

- 2 lo g_{9} (5) = - lo g_{9} (5^{2})

= lo g_{9} (2^{3}) - lo g_{9} (5^{2})

Apply log rule:

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

lo g_{9} (2^{3}) - lo g_{9} (5^{2}) = lo g_{9} (\frac{2 ^{3}}{5 ^{2}})

= lo g_{9} (\frac{2 ^{3}}{5 ^{2}})

\frac{2 ^{3}}{5 ^{2}} = \frac{8}{25}

= lo g_{9} (\frac{8}{25})

4 lo g_{2} (x) - \frac{1}{3} lo g_{2} (x^{2} + 1)

ln (\frac{5}{7})

4 lo g_{8} (12) - 4 lo g_{8} (4)

- \frac{3}{7} lo g_{2} (\frac{3}{7}) - \frac{4}{7} lo g_{2} (\frac{4}{7})

ln (a + b) + ln (a - b) - 5 ln (c)

What is 3log_{9}(2)-2log_{9}(5) ?
The solution to 3log_{9}(2)-2log_{9}(5) is log_{9}(8/25)