What is the answer to log_{x}(4)= 1/3 ?

The answer to log_{x}(4)= 1/3 is x=64

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log_{x}(4)= 1/3

lo g_{x} (4) = \frac{1}{3}

x = 64

Solution steps

lo g_{x} (4) = \frac{1}{3}

Apply log rules

\frac{1}{lo g _{4} ( x )} = \frac{1}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{4} (x) \cdot 1

Simplify

3 = lo g_{4} (x)

Apply log rules

64 = x

Switch sides

x = 64

Verify Solutions:

x = 64

True

The solution is

x = 64

lo g_{2} (x + 4) = 3 - lo g_{2} (x + 6)

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

2 ln (x) = ln (9) + 4

p, ln (p) = r t + c

lo g_{4} (x - 5) = 1 - lo g_{4} (x - 2)