What is log_{3}(32)-log_{3}(4) ?

The solution to log_{3}(32)-log_{3}(4) is 3log_{3}(2)

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simplify log_{3}(32)-log_{3}(4)

simplify

lo g_{3} (32) - lo g_{3} (4)

3 lo g_{3} (2)

Decimal Notation

1.89278 \dots

Solution steps

lo g_{3} (32) - lo g_{3} (4)

Apply log rule:

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

lo g_{3} (32) - lo g_{3} (4) = lo g_{3} (\frac{32}{4})

= lo g_{3} (\frac{32}{4})

Divide the numbers:

\frac{32}{4} = 8

= lo g_{3} (8)

Factor the number:

8 = 2^{3}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 3 lo g_{3} (2)

3 lo g_{9} (x) - \frac{1}{2} lo g_{9} (y) - 5 lo g_{9} (z - 4)

2 ln (a) - ln (2 b) + 3 ln (2)

\frac{1}{3} [lo g_{6} (x) + lo g_{6} (7)] - [lo g_{6} (y)]

lo g_{10} (100 x)

ln (5) - 2 ln (4)

What is log_{3}(32)-log_{3}(4) ?
The solution to log_{3}(32)-log_{3}(4) is 3log_{3}(2)