What is the answer to log_{x}(3)= 2/3 ?

The answer to log_{x}(3)= 2/3 is x=3sqrt(3)

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log_{x}(3)= 2/3

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

x = 33

Decimal

x = 5.19615 \dots

Solution steps

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

Apply log rules

\frac{1}{lo g _{3} ( x )} = \frac{2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Simplify

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

Switch sides

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

Divide both sides by

2

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

Apply log rules

x = 33

Verify Solutions:

x = 33

True

The solution is

x = 33

2 - 6 ln (x) = 10

ln (\frac{2}{x ^{5}}) = 0

lo g_{3} (x) = 61

x, t = ln (x)

2 ln (a) - ln (2) = ln (18)

What is the answer to log_{x}(3)= 2/3 ?
The answer to log_{x}(3)= 2/3 is x=3sqrt(3)
Solve for x: log_{x}(3)= 2/3
The solution is x=3sqrt(3)