What is the answer to log_{x}(4)=(-1)/2 ?

The answer to log_{x}(4)=(-1)/2 is x= 1/16

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log_{x}(4)=(-1)/2

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

x = \frac{1}{16}

Decimal Notation

x = 0.0625

Solution steps

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

Apply log rules

\frac{1}{lo g _{4} ( 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_{4} (x) (- 1)

Simplify

2 = - lo g_{4} (x)

Move

lo g_{4} (x)

to the left side

2 + lo g_{4} (x) = 0

Move

2

to the right side

lo g_{4} (x) = - 2

Apply log rules

x = \frac{1}{16}

Verify Solutions:

x = \frac{1}{16}

True

The solution is

x = \frac{1}{16}

62 = 10 lo g_{10} (\frac{85}{x})

lo g_{3} (x + 5) = lo g_{3} (15 - x)

ln (x + 2) = x

x, - lo g_{10} (x) = 6.63

lo g_{10} (1 - 3 x) = 1

What is the answer to log_{x}(4)=(-1)/2 ?
The answer to log_{x}(4)=(-1)/2 is x= 1/16
Solve for x: log_{x}(4)=(-1)/2
The solution is x= 1/16