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

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

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log_{b}(2)= 1/2

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

b = 4

Solution steps

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

Apply log rules

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

Simplify

2 = lo g_{2} (b)

Apply log rules

4 = b

Switch sides

b = 4

Verify Solutions:

b = 4

True

The solution is

b = 4

lo g_{3} (x) = \frac{ln ( x )}{3}

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

1400 = 800 + 200 lo g_{10} (x - 9)

lo g_{3} (x^{2} - 2) = 0

lo g_{a} (2) = 2