What is the answer to log_{x}(5)= 1/2 ?

The answer to log_{x}(5)= 1/2 is x=25

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log_{x}(5)= 1/2

lo g_{x} (5) = \frac{1}{2}

x = 25

Solution steps

lo g_{x} (5) = \frac{1}{2}

Apply log rules

\frac{1}{lo g _{5} ( 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_{5} (x) \cdot 1

Simplify

2 = lo g_{5} (x)

Apply log rules

25 = x

Switch sides

x = 25

Verify Solutions:

x = 25

True

The solution is

x = 25

4 = - lo g_{10} (x)

lo g_{9} (x) = \frac{1}{2}

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

x, ln (2 x - y - 4) = 0

ln (x - 5) + ln (x + 3) = 2 ln (3)