What is the answer to log_{b}(8)=-1/2 ?

The answer to log_{b}(8)=-1/2 is b= 1/64

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log_{b}(8)=-1/2

lo g_{b} (8) = - \frac{1}{2}

b = \frac{1}{64}

Decimal Notation

b = 0.015625

Solution steps

lo g_{b} (8) = - \frac{1}{2}

Apply log rules

\frac{1}{lo g _{8} ( 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_{8} (b) \cdot 1

Simplify

2 = - lo g_{8} (b)

Move

lo g_{8} (b)

to the left side

2 + lo g_{8} (b) = 0

Move

2

to the right side

lo g_{8} (b) = - 2

Apply log rules

b = \frac{1}{64}

Verify Solutions:

b = \frac{1}{64}

True

The solution is

b = \frac{1}{64}

1 + ln (3 x) = 0

lo g_{10} (x) = 0.17527

ln (7 x + 2) = 3

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

ln (x) = 1 + ln (x + 1)

What is the answer to log_{b}(8)=-1/2 ?
The answer to log_{b}(8)=-1/2 is b= 1/64
Solve for b: log_{b}(8)=-1/2
The solution is b= 1/64