What is the answer to log_{b}(9)=-1/3 ?

The answer to log_{b}(9)=-1/3 is b= 1/729

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log_{b}(9)=-1/3

lo g_{b} (9) = - \frac{1}{3}

b = \frac{1}{729}

Decimal Notation

b = 0.00137 \dots

Solution steps

lo g_{b} (9) = - \frac{1}{3}

Apply log rules

\frac{1}{lo g _{9} ( b )} = - \frac{1}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 3 = - lo g_{9} (b) \cdot 1

Simplify

3 = - lo g_{9} (b)

Move

lo g_{9} (b)

to the left side

3 + lo g_{9} (b) = 0

Move

3

to the right side

lo g_{9} (b) = - 3

Apply log rules

b = \frac{1}{729}

Verify Solutions:

b = \frac{1}{729}

True

The solution is

b = \frac{1}{729}

- lo g_{10} (x) = 2.8

- lo g_{10} (x) = 2.1

ln (5 - 2 x) = - 7

ln (5 - 2 x) = - 5

\frac{1}{x} = e^{l n (x)}

What is the answer to log_{b}(9)=-1/3 ?
The answer to log_{b}(9)=-1/3 is b= 1/729
Solve for b: log_{b}(9)=-1/3
The solution is b= 1/729