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

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

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

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

a = 2

Solution steps

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

Apply log rules

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Apply log rules

2 = a

Switch sides

a = 2

Verify Solutions:

a = 2

True

The solution is

a = 2

2 lo g_{5} (x) = 1 + lo g_{5} (6)

lo g_{2} (x + 1) + lo g_{2} (x + 3) = 5

2 lo g_{10} (x) - lo g_{10} (10) = 3

2 = lo g_{3} (x + 7)

e^{3} = ln (x)

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