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Question Number 167282 by abdurehime last updated on 11/Mar/22

$$\mathrm{solve}{\left(3^{\mathrm{x}}\right)}^2\times 4^{\mathrm{x}}=6\sqrt{6}$$

Answered by nurtani last updated on 11/Mar/22

$${\left(3^x\right)}^2\times 4^x=6\sqrt{6}$$$${\left(3^2\right)}^x\times 4^x=6\sqrt{6}$$$$9^x\times 4^x=6\sqrt{6}$$$${\left(9\times 4\right)}^x=6\sqrt{6}$$$${36}^x=\sqrt{216}$$$$6^{2x}=6^{\frac{3}{2}}\Rightarrow 2x=\frac{3}{2}\Rightarrow x=\frac{3}{4}$$$$$$

Answered by DrHZ last updated on 12/Mar/22

$$x=?$$$${\left(3\right)}^{2x}\times 2^{2x}=6\sqrt{6}$$$$3^{2x}\times 2^{2x}=6\sqrt{6}$$$${\left(3\times 2\right)}^{2x}=\sqrt{6^2\times 6}$$$${\left(6\right)}^{2x}=\sqrt{216}$$$$6^{2x}=6^{\frac{3}{2}}\Rightarrow 2x=\frac{3}{2}\Rightarrow 4x=3\Rightarrow x=\frac{3}{4}$$$$------------$$$$3^{2\frac{3}{4}}\times 2^{2\frac{3}{4}}=6\sqrt{6}\Rightarrow 3^{\frac{3}{2}}\times 2^{\frac{3}{2}}=6\sqrt{6}$$$${\left(3\times 2\right)}^{\frac{3}{2}}=6\sqrt{6}\Rightarrow {\left(6\right)}^{\frac{3}{2}}=6\sqrt{6}$$$$\sqrt{6\times 6^2=}6\sqrt{6}$$$$6\sqrt{6}=6\sqrt{6}$$$$DrHZ$$

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