|x+3|=3^x+1

解

∣ x + 3 ∣ = 3^{x} + 1

x = - \frac{W _{0} ( \frac{l n ( 3 )}{81} ) + 4 ln ( 3 )}{ln ( 3 )} or x = - \frac{W _{0} ( - \frac{l n ( 3 )}{9} ) + 2 ln ( 3 )}{ln ( 3 )} or x = 1

十進法表記

x = - 4.01218 \dots, x = - 1.87213 \dots, x = 1

解答ステップ

∣ x + 3 ∣ = 3^{x} + 1

正と負の区間を求める

x < - 3, x \geq - 3

各区間の不等式を解く

x = - \frac{W _{0} ( \frac{l n ( 3 )}{81} ) + 4 ln ( 3 )}{ln ( 3 )} or x = - \frac{W _{0} ( - \frac{l n ( 3 )}{9} ) + 2 ln ( 3 )}{ln ( 3 )} or x = 1

x = - \frac{W _{0} ( \frac{l n ( 3 )}{81} ) + 4 ln ( 3 )}{ln ( 3 )} or x = - \frac{W _{0} ( - \frac{l n ( 3 )}{9} ) + 2 ln ( 3 )}{ln ( 3 )} or x = 1