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

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

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log_{x}(3)= 1/2

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

x = 9

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)

Apply log rules

9 = x

Switch sides

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

1 = lo g_{10} (x)

0.4 = lo g_{10} (x)

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

2 lo g_{3} (x) - lo g_{3} (7 x) = 1

- 5 lo g_{3} (2 x) = - 5