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

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

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2log_{x}(2)=log_{2}(x)+1

2 lo g_{x} (2) = lo g_{2} (x) + 1

x = 2, x = \frac{1}{4}

Decimal Notation

x = 2, x = 0.25

Solution steps

2 lo g_{x} (2) = lo g_{2} (x) + 1

Apply log rules

\frac{2}{lo g _{2} ( x )} = lo g_{2} (x) + 1

Rewrite the equation with

lo g_{2} (x) = u

\frac{2}{u} = u + 1

Solve

\frac{2}{u} = u + 1 : u = 1, u = - 2

u = 1, u = - 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 1 : x = 2

Solve

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

x = 2, x = \frac{1}{4}

Verify Solutions:

x = 2

True

, x = \frac{1}{4}

True

The solutions are

x = 2, x = \frac{1}{4}

lo g_{8} (16) + lo g_{8} (x - 2) = 2

0.7 = - lo g_{10} (x)

x^{l o g_{10} (x)} = 1 0^{6} x

y, ln (y) = 3 + ln (x)

lo g_{10} (2) = lo g_{10} (x)

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