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

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

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log_{x}(16)= 1/2

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

x = 256

Solution steps

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

Apply log rules

\frac{1}{lo g _{16} ( x )} = \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} (x) \cdot 1

Simplify

2 = lo g_{16} (x)

Apply log rules

256 = x

Switch sides

x = 256

Verify Solutions:

x = 256

True

The solution is

x = 256

ln (x) = 8.077133955

ln (x^{2}) = ln^{2} (x)

lo g_{x} (3^{x}) = \frac{x}{2}

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

0.23 = ln (y)

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