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

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

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

The solution is x= 1/(e^{\frac{2ln(2)){3}}}

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

x = \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}}

Decimal Notation

x = 0.62996 \dots

Solution steps

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

Apply log rules

\frac{ln ( x )}{ln ( 2 x )} = - 2

Multiply both sides by

ln (2 x)

\frac{ln ( x )}{ln ( 2 x )} ln (2 x) = - 2 ln (2 x)

Simplify

ln (x) = - 2 ln (2 x)

Apply log rules

x = \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}}

Verify Solutions:

x = \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}}

True

The solution is

x = \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}}

3.28 = - lo g_{10} (x)

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

lo g_{3} (x) = 4 lo g_{10} (x) 3

lo g_{x} (10) = \frac{1}{2}

x, lo g_{x} (64) = 2

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