What is the answer to log_{b}(3)= 1/4 ?

The answer to log_{b}(3)= 1/4 is b=81

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log_{b}(3)= 1/4

lo g_{b} (3) = \frac{1}{4}

b = 81

Solution steps

lo g_{b} (3) = \frac{1}{4}

Apply log rules

\frac{1}{lo g _{3} ( b )} = \frac{1}{4}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 4 = lo g_{3} (b) \cdot 1

Simplify

4 = lo g_{3} (b)

Apply log rules

81 = b

Switch sides

b = 81

Verify Solutions:

b = 81

True

The solution is

b = 81

n lo g_{10} (n) = 3.6 \cdot 1 0^{13}

lo g_{2} (x) + 4 = 5 lo g_{x} (2)

ln (x) - ln (2 x + 1) = 1

y, ln (y) = ln (x)

7 = a lo g_{\frac{1}{3}} (4 x - 8) - 3