What is the answer to 2^{log_{3}(x)}=x^{log_{3}(2)},x>0 ?

The answer to 2^{log_{3}(x)}=x^{log_{3}(2)},x>0 is x>0

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2^{log_{3}(x)}=x^{log_{3}(2)},x>0

2^{l o g_{3} (x)} = x^{l o g_{3} (2)}, x > 0

x > 0

Solution steps

2^{l o g_{3} (x)} = x^{l o g_{3} (2)}

Apply log rules

\frac{lo g _{3} ( x ) lo g _{3} ( 2 )}{0.63092 \dots} = \frac{lo g _{3} ( 2 ) lo g _{3} ( x )}{0.63092 \dots}

Rewrite the equation with

lo g_{3} (x) = u

\frac{u lo g _{3} ( 2 )}{0.63092 \dots} = \frac{lo g _{3} ( 2 ) u}{0.63092 \dots}

Solve

\frac{u lo g _{3} ( 2 )}{0.63092 \dots} = \frac{lo g _{3} ( 2 ) u}{0.63092 \dots} :

True for all

u

True for all u

Verify Solutions:

x > 0

True

The solution is

x > 0

Check constrains

x > 0

a, ln (8 a) = 2 ln (a + 2 b) - ln (b)

a, lo g_{3} (a) + 1 = 2 lo g_{10} (9) (b)

lo g_{10} (x + 2) - lo g_{10} (9) = lo g_{10} (15)

lo g_{10} (x) = - 1

lo g_{10} (x) = - 5

What is the answer to 2^{log_{3}(x)}=x^{log_{3}(2)},x>0 ?
The answer to 2^{log_{3}(x)}=x^{log_{3}(2)},x>0 is x>0
Solve for x: 2^{log_{3}(x)}=x^{log_{3}(2)},x>0
The solution is x>0