What is the answer to log_{b}(8)= 3/2 ?

The answer to log_{b}(8)= 3/2 is b=4

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log_{b}(8)= 3/2

lo g_{b} (8) = \frac{3}{2}

b = 4

Solution steps

lo g_{b} (8) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{8} ( 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_{8} (b) \cdot 3

Simplify

2 = lo g_{8} (b) \cdot 3

Switch sides

lo g_{8} (b) \cdot 3 = 2

Divide both sides by

3

lo g_{8} (b) = \frac{2}{3}

Apply log rules

b = 4

Verify Solutions:

b = 4

True

The solution is

b = 4

x, ln (x^{2} + 4 y^{2}) = 0

lo g_{x} (x + 6) = 2

2 lo g_{4} (x) - lo g_{4} (x + 24) = 1

2 lo g_{10} (x) = lo g_{10} (5 x + 6)

2 ln (8 x + 9) - 1 = - 5