What is the answer to log_{x}(9)= 3/2 ?

The answer to log_{x}(9)= 3/2 is x=9^{2/3}

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log_{x}(9)= 3/2

lo g_{x} (9) = \frac{3}{2}

x = 9^{\frac{2}{3}}

Decimal Notation

x = 4.32674 \dots

Solution steps

lo g_{x} (9) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{9} ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{9} (x) \cdot 3

Simplify

2 = lo g_{9} (x) \cdot 3

Switch sides

lo g_{9} (x) \cdot 3 = 2

Divide both sides by

3

lo g_{9} (x) = \frac{2}{3}

Apply log rules

x = 9^{\frac{2}{3}}

Verify Solutions:

x = 9^{\frac{2}{3}}

True

The solution is

x = 9^{\frac{2}{3}}

ln (x) = ln (x + 1) - ln (2)

50 = 7.3718 ln (x) + 32.666

\frac{9}{5 ln ( x ^{2} - 3 )} = 4

lo g_{7} (x - 5) + lo g_{7} (3 x - 1) = 2

x - 2 x ln (x) = 0

What is the answer to log_{x}(9)= 3/2 ?
The answer to log_{x}(9)= 3/2 is x=9^{2/3}
Solve for x: log_{x}(9)= 3/2
The solution is x=9^{2/3}