What is 1/2 log_{3}(64)-2log_{3}(4)+log_{3}(18) ?

The solution to 1/2 log_{3}(64)-2log_{3}(4)+log_{3}(18) is 2

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simplify 1/2 log_{3}(64)-2log_{3}(4)+log_{3}(18)

simplify

\frac{1}{2} lo g_{3} (64) - 2 lo g_{3} (4) + lo g_{3} (18)

2

Solution steps

\frac{1}{2} lo g_{3} (64) - 2 lo g_{3} (4) + lo g_{3} (18)

\frac{1}{2} lo g_{3} (64) = lo g_{3} (6 4^{\frac{1}{2}})

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

= lo g_{3} (6 4^{\frac{1}{2}}) - lo g_{3} (4^{2}) + lo g_{3} (18)

Apply log rule:

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

lo g_{3} (6 4^{\frac{1}{2}}) - lo g_{3} (4^{2}) = lo g_{3} (\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}})

= lo g_{3} (\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}}) + lo g_{3} (18)

Apply log rule:

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

lo g_{3} (\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}}) + lo g_{3} (18) = lo g_{3} (\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}} \cdot 18)

= lo g_{3} (\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}} \cdot 18)

\frac{6 4 ^{\frac{1}{2}}}{4 ^{2}} \cdot 18 = 9

= lo g_{3} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

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

= 2

\frac{1}{2} (lo g_{10} (x) + lo g_{10} (9))

0.491 \cdot lo g_{10} (21) - 0.491 \cdot lo g_{10} (20)

lo g_{x} (x^{2} y)

- \frac{3}{6} lo g_{10} (\frac{3}{6}) - \frac{3}{6} lo g_{10} (\frac{3}{6})

ln (\frac{e ^{2}}{9})

What is 1/2 log_{3}(64)-2log_{3}(4)+log_{3}(18) ?
The solution to 1/2 log_{3}(64)-2log_{3}(4)+log_{3}(18) is 2