What is the answer to log_{x}(3)=-1/2 ?

The answer to log_{x}(3)=-1/2 is x= 1/9

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log_{x}(3)=-1/2

lo g_{x} (3) = - \frac{1}{2}

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

lo g_{x} (3) = - \frac{1}{2}

Apply log rules

\frac{1}{lo g _{3} ( x )} = - \frac{1}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 2 = - lo g_{3} (x) \cdot 1

Simplify

2 = - lo g_{3} (x)

Move

lo g_{3} (x)

to the left side

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

Move

2

to the right side

lo g_{3} (x) = - 2

Apply log rules

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

0.4 = lo g_{10} (y)

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

75 = 20 lo g_{10} (\frac{800}{x})

lo g_{2} (8 x + 5) = 5

6 + 7 \cdot lo g_{2} (x) = 21