What is the answer to log_{x}(4)=log_{2}(x) ?

The answer to log_{x}(4)=log_{2}(x) is x=2^{sqrt(2)},x= 1/(2^{sqrt(2))}

Solve for x: log_{x}(4)=log_{2}(x)

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

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

x = 2^{2}, x = \frac{1}{2 ^{2}}

Decimal Notation

x = 2.66514 \dots, x = 0.37521 \dots

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

\frac{2}{u} = u

Solve

\frac{2}{u} = u : u = 2, u = - 2

u = 2, u = - 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 2 : x = 2^{2}

Solve

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

x = 2^{2}, x = \frac{1}{2 ^{2}}

Verify Solutions:

x = 2^{2}

True

, x = \frac{1}{2 ^{2}}

True

The solutions are

x = 2^{2}, x = \frac{1}{2 ^{2}}

5 lo g_{9} (a) = lo g_{9} (x)

lo g_{x} (3) + lo g_{x} (27) = 2

x, f = lo g_{g} (x)

lo g_{10} (10 a) = 1.5

10 \cdot lo g_{10} (x^{2}) = 2

What is the answer to log_{x}(4)=log_{2}(x) ?
The answer to log_{x}(4)=log_{2}(x) is x=2^{sqrt(2)},x= 1/(2^{sqrt(2))}
Solve for x: log_{x}(4)=log_{2}(x)
The solution is x=2^{sqrt(2)},x= 1/(2^{sqrt(2))}