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Question Number 167107 by mathlove last updated on 06/Mar/22

Answered by alephzero last updated on 06/Mar/22

$$a^{b^x}=a^{\sqrt[3]{\frac{b}{b^x}}}$$$$\Rightarrow b^x=\sqrt[3]{\frac{b}{b^x}}$$$$\Rightarrow b^x=\sqrt[3]{b^{1-x}}$$$$\Rightarrow b^x=b^{\frac{1-x}{3}}$$$$\Rightarrow x=\frac{1-x}{3}$$$$\Rightarrow 3x=1-x$$$$\Rightarrow 4x=1$$$$\Rightarrow x=\frac{1}{4}$$

Commented by peter frank last updated on 06/Mar/22

$$\mathrm{great}$$

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