Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4 - Page 493: 146

$x = 1$ or $x = e^2$

Work Step by Step

$$(\ln x)^2 = \ln x^2$$ $$(\ln x)^2 = 2\ln x$$ Let $\ln x = a$. We can now re-write the above equation as follows: $$a^2 = 2a$$ $$a^2 - 2a = 0$$ $$a(a - 2) = 0$$ $$a = 0$$ $$OR$$ $$a = 2$$ Substituting back the original values: $$\ln x = 0$$ $$e^0 = x$$ $$1 = x$$ $$OR$$ $$\ln x = 2$$ $$e^2 = x$$

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