What is the answer to log_{x}(sqrt(8))= 3/2 ?

The answer to log_{x}(sqrt(8))= 3/2 is x=2

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log_{x}(sqrt(8))= 3/2

lo g_{x} (8) = \frac{3}{2}

x = 2

Solution steps

lo g_{x} (8) = \frac{3}{2}

Apply log rules

\frac{ln ( 8 )}{ln ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (8) \cdot 2 = ln (x) \cdot 3

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

ln (x) = - a

3 lo g_{10} (2 y) = - 6

0 = ln (x) - \frac{1}{2} x + 1

3 ln (x) - 1 = 0

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

What is the answer to log_{x}(sqrt(8))= 3/2 ?
The answer to log_{x}(sqrt(8))= 3/2 is x=2
Solve for x: log_{x}(sqrt(8))= 3/2
The solution is x=2