What is 1/2 log_{3}(9x)+3/2 log_{3}(4x^3) ?

The solution to 1/2 log_{3}(9x)+3/2 log_{3}(4x^3) is 1+(log_{3}(64x^{10}))/2

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simplify 1/2 log_{3}(9x)+3/2 log_{3}(4x^3)

simplify

\frac{1}{2} lo g_{3} (9 x) + \frac{3}{2} lo g_{3} (4 x^{3})

1 + \frac{lo g _{3} ( 64 x ^{10} )}{2}

Solution steps

\frac{1}{2} lo g_{3} (9 x) + \frac{3}{2} lo g_{3} (4 x^{3})

Simplify

\frac{1}{2} lo g_{3} (9 x) : 1 + \frac{lo g _{3} ( x )}{2}

= 1 + \frac{lo g _{3} ( x )}{2} + \frac{3}{2} lo g_{3} (4 x^{3})

Simplify

\frac{3}{2} lo g_{3} (4 x^{3}) : \frac{3 lo g _{3} ( 4 x ^{3} )}{2}

= 1 + \frac{lo g _{3} ( x )}{2} + \frac{3 lo g _{3} ( 4 x ^{3} )}{2}

Join

1 + \frac{lo g _{3} ( x )}{2} + \frac{3 lo g _{3} ( 4 x ^{3} )}{2} : 1 + \frac{lo g _{3} ( x ) + 3 lo g _{3} ( 4 x ^{3} )}{2}

= 1 + \frac{lo g _{3} ( x ) + 3 lo g _{3} ( 4 x ^{3} )}{2}

Simplify

lo g_{3} (x) + 3 lo g_{3} (4 x^{3}) : lo g_{3} (64 x^{10})

= 1 + \frac{lo g _{3} ( 64 x ^{10} )}{2}

lo g_{12} (\frac{12}{y})

3 lo g_{10} (6) - 4 lo g_{10} (2) - lo g_{10} (3)

lo g_{2} (\frac{x y ^{2}}{64})

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

12 lo g_{7} (x) - 3 lo g_{7} (y)

What is 1/2 log_{3}(9x)+3/2 log_{3}(4x^3) ?
The solution to 1/2 log_{3}(9x)+3/2 log_{3}(4x^3) is 1+(log_{3}(64x^{10}))/2