What is the answer to log_{x}(sqrt(3))= 1/6 ?

The answer to log_{x}(sqrt(3))= 1/6 is x=27

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log_{x}(sqrt(3))= 1/6

lo g_{x} (3) = \frac{1}{6}

x = 27

Solution steps

lo g_{x} (3) = \frac{1}{6}

Apply log rules

\frac{ln ( 3 )}{ln ( x )} = \frac{1}{6}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (3) \cdot 6 = ln (x) \cdot 1

Apply log rules

27 = x

Switch sides

x = 27

Verify Solutions:

x = 27

True

The solution is

x = 27

x^{1 + l o g_{7} (x)} = 7 x

lo g_{10} (33 - x) = 1 + lo g_{10} (x)

3 lo g_{x} (3) = 8 - 4 lo g_{3} (x)

lo g_{3} (lo g_{2} (x)) = - 1

3 ln (x) = ln (216)

What is the answer to log_{x}(sqrt(3))= 1/6 ?
The answer to log_{x}(sqrt(3))= 1/6 is x=27
Solve for x: log_{x}(sqrt(3))= 1/6
The solution is x=27