What is the answer to log_{b}(3)= 1/2 ?

The answer to log_{b}(3)= 1/2 is b=9

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log_{b}(3)= 1/2

lo g_{b} (3) = \frac{1}{2}

b = 9

Solution steps

lo g_{b} (3) = \frac{1}{2}

Apply log rules

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

Simplify

2 = lo g_{3} (b)

Apply log rules

9 = b

Switch sides

b = 9

Verify Solutions:

b = 9

True

The solution is

b = 9

ln ((2 x + 3)^{3}) = 1

\frac{lo g _{10} ( 2 x ^{2} + 1 )}{lo g _{10} ( x + 1 )} = 2

40 = 20 \cdot lo g_{10} (\frac{x}{0.0002})

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

lo g_{10} (c) = 0