What is the answer to log_{b}(343)=-3/2 ?

The answer to log_{b}(343)=-3/2 is b= 1/49

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log_{b}(343)=-3/2

lo g_{b} (343) = - \frac{3}{2}

b = \frac{1}{49}

Decimal Notation

b = 0.02040 \dots

Solution steps

lo g_{b} (343) = - \frac{3}{2}

Apply log rules

\frac{1}{lo g _{343} ( b )} = - \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = - lo g_{343} (b) \cdot 3

Simplify

2 = - lo g_{343} (b) \cdot 3

Switch sides

- lo g_{343} (b) \cdot 3 = 2

Divide both sides by

- 3

lo g_{343} (b) = - \frac{2}{3}

Apply log rules

b = \frac{1}{49}

Verify Solutions:

b = \frac{1}{49}

True

The solution is

b = \frac{1}{49}

lo g_{a} (64) = 2

lo g_{9} (2 x - 7) = \frac{3}{2}

3 lo g_{8} (x) - lo g_{x} (64 + 1) = 0

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

ln (4 x) + 1 = 0

What is the answer to log_{b}(343)=-3/2 ?
The answer to log_{b}(343)=-3/2 is b= 1/49
Solve for b: log_{b}(343)=-3/2
The solution is b= 1/49