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

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

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log_{b}(2)=-1/2

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

b = \frac{1}{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)

Move

lo g_{2} (b)

to the left side

2 + lo g_{2} (b) = 0

Move

2

to the right side

lo g_{2} (b) = - 2

Apply log rules

b = \frac{1}{4}

Verify Solutions:

b = \frac{1}{4}

True

The solution is

b = \frac{1}{4}

2 ln (y) = 12

ln (3 x - 17) = 8

ln (3 x - 17) = 3

ln (3 x - 17) = 6

ln (3 x - 17) = 7