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

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

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log_{a}(2)= 1/2

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

a = 4

Solution steps

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

Apply log rules

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

Simplify

2 = lo g_{2} (a)

Apply log rules

4 = a

Switch sides

a = 4

Verify Solutions:

a = 4

True

The solution is

a = 4

lo g_{10} (x + 9) = 2 + lo g_{10} (x)

lo g_{3} (- 2 x + 8) = 1

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

2 lo g_{4} (x) + lo g_{x} (4) = 3

lo g_{4} (x) + lo g_{4} (x - 3) = 1