What is the answer to log_{x}(1/512)=-3/2 ?

The answer to log_{x}(1/512)=-3/2 is x=64

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log_{x}(1/512)=-3/2

lo g_{x} (\frac{1}{512}) = - \frac{3}{2}

x = 64

Solution steps

lo g_{x} (\frac{1}{512}) = - \frac{3}{2}

Apply log rules

\frac{ln ( \frac{1}{512} )}{ln ( x )} = - \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (\frac{1}{512}) \cdot 2 = - ln (x) \cdot 3

Apply log rules

x = 64

Verify Solutions:

x = 64

True

The solution is

x = 64

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

lo g_{5} (x^{2} + 9) = 2

x, z = ln (x^{2}) + 2 x y - 2 y

lo g_{10} (x + 7) = lo g_{10} (x) + lo g_{10} (7)

lo g_{10} (2 x + 50) = 2

What is the answer to log_{x}(1/512)=-3/2 ?
The answer to log_{x}(1/512)=-3/2 is x=64
Solve for x: log_{x}(1/512)=-3/2
The solution is x=64