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

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

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

The solution is x=2^{sqrt(log_{2)(3)}},x= 1/(2^{sqrt(log_{2)(3))}}

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

x = 2^{l o g_{2} (3)}, x = \frac{1}{2 ^{l o g_{2} (3)}}

Decimal Notation

x = 2.39321 \dots, x = 0.41784 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

\frac{lo g _{2} ( 3 )}{u} = u : u = lo g_{2} (3), u = - lo g_{2} (3)

u = lo g_{2} (3), u = - lo g_{2} (3)

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

lo g_{2} (x) = - lo g_{2} (3) : x = \frac{1}{2 ^{l o g_{2} (3)}}

x = 2^{l o g_{2} (3)}, x = \frac{1}{2 ^{l o g_{2} (3)}}

Verify Solutions:

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

True

, x = \frac{1}{2 ^{l o g_{2} (3)}}

True

The solutions are

x = 2^{l o g_{2} (3)}, x = \frac{1}{2 ^{l o g_{2} (3)}}

x, lo g_{10} (x + 1) = 5

lo g_{7} (x) = lo g_{7} (20)

lo g_{4} (x^{2} + 60) = 2

2.12 = - lo g_{10} (x)

9000 = \frac{4000}{ln ( x + 10 )}

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