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

The answer to log_{a}(sqrt(a))= 1/2 is 0 1

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

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

0 < a < 1 or a > 1

Solution steps

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

Apply log rules

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Simplify

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

Apply log rules

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

Rewrite the equation with

ln (a) = u

\frac{1}{2} u \cdot 2 = u

Solve

\frac{1}{2} u \cdot 2 = u :

True for all

u

True for all u

Verify Solutions:

0 < a < 1

True

, a > 1

True

The solution is

0 < a < 1 or a > 1

lo g_{3} (4 x + 4) - lo g_{3} (2 - x) = 1

ln (x + 2) - ln (x - 1) = ln (4)

lo g_{8} (16) + lo g_{8} (y - 2) = 2

lo g_{a} (x) = b

4 lo g_{3} (x) - 11 = 5

What is the answer to log_{a}(sqrt(a))= 1/2 ?
The answer to log_{a}(sqrt(a))= 1/2 is 0<a<1\lor a>1
Solve for a: log_{a}(sqrt(a))= 1/2
The solution is 0<a<1\lor a>1