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

The answer to log_{x}(2)=-1 is x= 1/2

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log_{x}(2)=-1

lo g_{x} (2) = - 1

x = \frac{1}{2}

Decimal

x = 0.5

Solution steps

lo g_{x} (2) = - 1

Apply log rules

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

Multiply both sides by

lo g_{2} (x)

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

Simplify

1 = - lo g_{2} (x)

Move

lo g_{2} (x)

to the left side

1 + lo g_{2} (x) = 0

Move

1

to the right side

lo g_{2} (x) = - 1

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

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

c + 5 ln (- 1 + c) = 0.540302

lo g_{8} (x) = \frac{1}{6}

lo g_{3} (x - 9) = 4

lo g_{2} (x) + lo g_{2} (2 x) = lo g_{3} (9)