What is the answer to log_{a}(sqrt(2))= 1/6 ?

The answer to log_{a}(sqrt(2))= 1/6 is a=8

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log_{a}(sqrt(2))= 1/6

lo g_{a} (2) = \frac{1}{6}

a = 8

Solution steps

lo g_{a} (2) = \frac{1}{6}

Apply log rules

\frac{ln ( 2 )}{ln ( a )} = \frac{1}{6}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (2) \cdot 6 = ln (a) \cdot 1

Apply log rules

8 = a

Switch sides

a = 8

Verify Solutions:

a = 8

True

The solution is

a = 8

ln^{2} (x) = ln (e)

2 lo g_{10} (x - 2) = 2 x - 7

lo g_{x} (64) + 3 \cdot lo g_{4} (x) - lo g_{x} (4) = 5

lo g_{27} (x) = 3

\frac{1}{2 lo g _{10} ( 7 x - 3 )} = - 5

What is the answer to log_{a}(sqrt(2))= 1/6 ?
The answer to log_{a}(sqrt(2))= 1/6 is a=8
Solve for a: log_{a}(sqrt(2))= 1/6
The solution is a=8