What is the answer to 3log_{2}(x)-2log_{3}(x)=1 ?

The answer to 3log_{2}(x)-2log_{3}(x)=1 is x=3^{(log_{3}(2))/(3-2log_{3)(2)}}

Solve for x: 3log_{2}(x)-2log_{3}(x)=1

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

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3 lo g_{2} (x) - 2 lo g_{3} (x) = 1

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

Decimal Notation

x = 1.49001 \dots

Solution steps

3 lo g_{2} (x) - 2 lo g_{3} (x) = 1

Apply log rules

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

Verify Solutions:

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

True

The solution is

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

lo g_{3} (- 2 x) + lo g_{3} (12) = 3

lo g_{7} (x) = \frac{1}{2}

ln (x) = - \frac{3 x}{e} + 4

lo g_{4} (x) - 2 lo g_{x} (4) = 1

1 + ln (x) = ln (6)

What is the answer to 3log_{2}(x)-2log_{3}(x)=1 ?
The answer to 3log_{2}(x)-2log_{3}(x)=1 is x=3^{(log_{3}(2))/(3-2log_{3)(2)}}
Solve for x: 3log_{2}(x)-2log_{3}(x)=1
The solution is x=3^{(log_{3}(2))/(3-2log_{3)(2)}}