What is the answer to log_{a}(16)= 1/2 ?

The answer to log_{a}(16)= 1/2 is a=256

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log_{a}(16)= 1/2

lo g_{a} (16) = \frac{1}{2}

a = 256

Solution steps

lo g_{a} (16) = \frac{1}{2}

Apply log rules

\frac{1}{lo g _{16} ( a )} = \frac{1}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{16} (a) \cdot 1

Simplify

2 = lo g_{16} (a)

Apply log rules

256 = a

Switch sides

a = 256

Verify Solutions:

a = 256

True

The solution is

a = 256

lo g_{3} (5) + lo g_{3} (x - 4) = 2

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

10 lo g_{10} (x) = 3

lo g_{8} (3 x - 2) = 2

2 \cdot lo g_{10} (3 - x) = - 1

What is the answer to log_{a}(16)= 1/2 ?
The answer to log_{a}(16)= 1/2 is a=256
Solve for a: log_{a}(16)= 1/2
The solution is a=256