What is the answer to log_{x}(6)= 1/2 ?

The answer to log_{x}(6)= 1/2 is x=36

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log_{x}(6)= 1/2

lo g_{x} (6) = \frac{1}{2}

x = 36

Solution steps

lo g_{x} (6) = \frac{1}{2}

Apply log rules

\frac{1}{lo g _{6} ( 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_{6} (x) \cdot 1

Simplify

2 = lo g_{6} (x)

Apply log rules

36 = x

Switch sides

x = 36

Verify Solutions:

x = 36

True

The solution is

x = 36

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

ln (x) + ln (7 x + 1) = 1

lo g_{5} (n^{2} + 20 n) = 3

lo g_{2} (x - 5) = 2 - lo g_{2} (x - 8)

ln (x^{2}) - 0.7 = 0