What is the answer to log_{b}(6)= 1/4 ?

The answer to log_{b}(6)= 1/4 is b=1296

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log_{b}(6)= 1/4

lo g_{b} (6) = \frac{1}{4}

b = 1296

Solution steps

lo g_{b} (6) = \frac{1}{4}

Apply log rules

\frac{1}{lo g _{6} ( 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_{6} (b) \cdot 1

Simplify

4 = lo g_{6} (b)

Apply log rules

1296 = b

Switch sides

b = 1296

Verify Solutions:

b = 1296

True

The solution is

b = 1296

ln (lo g_{10} (1 - x)) = 0

ln (8 x) - 2 ln (x^{4}) = 0

lo g_{2} (x^{2} - 2 x) = 8

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

11 lo g_{10} (z) = 11