# How do you solve 11^(x^2) =25.4?

Mar 17, 2016

$x = 1.1614$ or $x = - 1.1614$

#### Explanation:

Taking log of both the sides in the equation ${11}^{{x}^{2}} = 25.4$,

${x}^{2} \times \log 11 = \log 25.4$ or

${x}^{2} = \frac{\log 25.4}{\log} 11 = \frac{1.4048}{1.0414} = 1.349$

Hence $x = \pm 1.1614$ i.e. $x = 1.1614$ or $x = - 1.1614$