What is the answer to 2log_{3}(x)=3log_{2}(3) ?

The answer to 2log_{3}(x)=3log_{2}(3) is x=3^{(3log_{2}(3))/2}

Solve for x: 2log_{3}(x)=3log_{2}(3)

The solution is x=3^{(3log_{2}(3))/2}

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

x = 3^{\frac{3 l o g _{2} ( 3 )}{2}}

Decimal Notation

x = 13.62476 \dots

Solution steps

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

Divide both sides by

2

lo g_{3} (x) = \frac{3 lo g _{2} ( 3 )}{2}

Apply log rules

x = 3^{\frac{3 l o g _{2} ( 3 )}{2}}

Verify Solutions:

x = 3^{\frac{3 l o g _{2} ( 3 )}{2}}

True

The solution is

x = 3^{\frac{3 l o g _{2} ( 3 )}{2}}

lo g_{3} (x) = 1.5

lo g_{6} (x^{2} + 5 x) = 2

ln (3 x + e) = 7

lo g_{x} (256) = 2

lo g_{2} (6 x - 8) - lo g_{2} (8) = 1

What is the answer to 2log_{3}(x)=3log_{2}(3) ?
The answer to 2log_{3}(x)=3log_{2}(3) is x=3^{(3log_{2}(3))/2}
Solve for x: 2log_{3}(x)=3log_{2}(3)
The solution is x=3^{(3log_{2}(3))/2}