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

The solution to 2log_{a}(3)-2log_{a}(2) is log_{a}(9/4)

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

simplify

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

lo g_{a} (\frac{9}{4})

Solution steps

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

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

- 2 lo g_{a} (2) = - lo g_{a} (2^{2})

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

Apply log rule:

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

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

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

\frac{3 ^{2}}{2 ^{2}} = \frac{9}{4}

= lo g_{a} (\frac{9}{4})

ln (2) - ln (x)

\frac{1}{4} ln (x) + 5 [ln (x - 2) - \frac{3}{10} ln (x + 2)]

8 ln (x) - \frac{1}{9} ln (y)

lo g_{10} (\frac{x}{z ^{6}})

lo g_{10} (28) - lo g_{10} (7)

What is 2log_{a}(3)-2log_{a}(2) ?
The solution to 2log_{a}(3)-2log_{a}(2) is log_{a}(9/4)