What is log_{3/2}(9)+log_{3/2}(3)-log_{3/2}(8) ?

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

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simplify log_{3/2}(9)+log_{3/2}(3)-log_{3/2}(8)

simplify

lo g_{\frac{3}{2}} (9) + lo g_{\frac{3}{2}} (3) - lo g_{\frac{3}{2}} (8)

3

Solution steps

lo g_{\frac{3}{2}} (9) + lo g_{\frac{3}{2}} (3) - lo g_{\frac{3}{2}} (8)

Apply log rule:

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

lo g_{\frac{3}{2}} (9) + lo g_{\frac{3}{2}} (3) = lo g_{\frac{3}{2}} (9 \cdot 3)

= lo g_{\frac{3}{2}} (9 \cdot 3) - lo g_{\frac{3}{2}} (8)

Apply log rule:

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

lo g_{\frac{3}{2}} (9 \cdot 3) - lo g_{\frac{3}{2}} (8) = lo g_{\frac{3}{2}} (\frac{9 \cdot 3}{8})

= lo g_{\frac{3}{2}} (\frac{9 \cdot 3}{8})

Multiply the numbers:

9 \cdot 3 = 27

= lo g_{\frac{3}{2}} (\frac{27}{8})

Factor the number:

\frac{27}{8} = (\frac{3}{2})^{3}

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

Apply log rule:

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

= 3

ln (\frac{e ^{2}}{13})

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

lo g_{4} (x y^{5} z^{4})

lo g_{10} (\frac{a ^{2} b}{c})

ln (\frac{e ^{2}}{14})

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