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

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

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log_{x}(2)= 1/2

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

x = 4

Solution steps

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

Apply log rules

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

Simplify

2 = lo g_{2} (x)

Apply log rules

4 = x

Switch sides

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

lo g_{2} (x - 2) = 2 - lo g_{2} (x - 5)

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

lo g_{10} (3 x + 7) = 0

2 lo g_{10} (3 x - 7) = 8

2 ln (x) + 3 = 0