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f Logx (1 / 8) = - 3 / 2, then x is equal to


If Logx (1 / 8) = - 3 / 2, then x is equal to 

Solution 

Rewrite the logarithmic equations using exponential equation 

x- 3 / 2 = 1 / 8 

The above equation may be rewritten as 

x - 3 / 2 = 1 / 23 = 2-3

(√x)-3 = 2-3

The above equation gives 

√x = 2 or x = 4 

Guest Jun 12, 2017
 #1
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You don't understand?

\(\log_x\dfrac{1}{8}=-\dfrac{3}{2}\\ x^{\log_x1/8}=x^{-3/2}\\ \dfrac{1}{8}=x^{-3/2}\\ x^{3/2}=8\\ \sqrt[3]{x^{3/2}}=\sqrt[3]{8}\\ x^{1/2}=2\\ x = 2^2 = 4\)

MaxWong  Jun 12, 2017

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