What is the answer to 2log_{3}(x)=3log_{3}(5) ?

The answer to 2log_{3}(x)=3log_{3}(5) is x=3^{(3log_{3}(5))/2}

Solve for x: 2log_{3}(x)=3log_{3}(5)

The solution is x=3^{(3log_{3}(5))/2}

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2 lo g_{3} (x) = 3 lo g_{3} (5)

x = 3^{\frac{3 l o g _{3} ( 5 )}{2}}

Decimal Notation

x = 11.18033 \dots

Solution steps

2 lo g_{3} (x) = 3 lo g_{3} (5)

Divide both sides by

2

lo g_{3} (x) = \frac{3 lo g _{3} ( 5 )}{2}

Apply log rules

x = 3^{\frac{3 l o g _{3} ( 5 )}{2}}

Verify Solutions:

x = 3^{\frac{3 l o g _{3} ( 5 )}{2}}

True

The solution is

x = 3^{\frac{3 l o g _{3} ( 5 )}{2}}

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

ln (2 x) = 4 ln (4 x)

ln (- 3 x - 1) - ln (7) = 2

lo g_{5} (x - 3) = 1 - lo g_{5} (x - 7)

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

What is the answer to 2log_{3}(x)=3log_{3}(5) ?
The answer to 2log_{3}(x)=3log_{3}(5) is x=3^{(3log_{3}(5))/2}
Solve for x: 2log_{3}(x)=3log_{3}(5)
The solution is x=3^{(3log_{3}(5))/2}