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

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

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log_{a}(2)=-1

lo g_{a} (2) = - 1

a = \frac{1}{2}

Decimal

a = 0.5

Solution steps

lo g_{a} (2) = - 1

Apply log rules

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

Multiply both sides by

lo g_{2} (a)

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

Simplify

1 = - lo g_{2} (a)

Move

lo g_{2} (a)

to the left side

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

Move

1

to the right side

lo g_{2} (a) = - 1

Apply log rules

a = \frac{1}{2}

Verify Solutions:

a = \frac{1}{2}

True

The solution is

a = \frac{1}{2}

1.7 = - lo g_{10} (x)

- 5 - 2 lo g_{4} (- 10 x + 1) = - 11

x, 2 lo g_{3} (2 x - 3) = 4

ln (5 x) + 1 = 0

20 lo g_{10} (x) = - 1