What is the answer to log_{x}(3)=-1 ?

The answer to log_{x}(3)=-1 is x= 1/3

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log_{x}(3)=-1

lo g_{x} (3) = - 1

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

lo g_{x} (3) = - 1

Apply log rules

\frac{1}{lo g _{3} ( x )} = - 1

Multiply both sides by

lo g_{3} (x)

\frac{1}{lo g _{3} ( x )} lo g_{3} (x) = - 1 \cdot lo g_{3} (x)

Simplify

1 = - lo g_{3} (x)

Move

lo g_{3} (x)

to the left side

1 + lo g_{3} (x) = 0

Move

1

to the right side

lo g_{3} (x) = - 1

Apply log rules

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

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

lo g_{6} (4 x^{2}) - lo g_{6} (x) = 2

ln (x) = - 7

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

lo g_{3} (x + 9) = 1