Alg9.4.27

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Find the value of x when x^{\log_3(x^2)+(\log_3(x))^{2}-10}=\frac{1}{x^2}\,

Let \log_a x=a\,

Hence

x^{2a+a^2-10}=\frac{1}{x^2}\,

Equating the powers

a^2+2a-8=0\,

(a+4)(a-2)=0\,

Hence a=-4 or a=-2

Now

x=3^a\,

The values of x are 1/81,9.


Main Page:Algebra:Logarithmic

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