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

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

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

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

a = 6

Solution steps

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

Apply log rules

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Apply log rules

6 = a

Switch sides

a = 6

Verify Solutions:

a = 6

True

The solution is

a = 6

y, ln (y) = 2 t - 3

lo g_{3} (25) = 2 lo g_{3} (x)

lo g_{10} (x - 2) = 0

- c + 1 + c ln (c) = 1

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

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