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Question Number 192676 by Shrinava last updated on 24/May/23

$$\mathrm{Find}:\mathrm{x}=?$$$$1.\lg ({5\mathrm{x}}^2-6)\cdot \lg (5\mathrm{x}-6)=0$$$$2.(2\mathrm{x}-5)\cdot {\log }_3(1,5-\mathrm{x})=0$$$$3.4^{\mathbf{x}}-14\cdot 2^{\mathbf{x}}-32=0$$

Answered by Frix last updated on 24/May/23

$$1.5x^2-6=1\vee 5x-6=1\Rightarrow x=\pm \frac{\sqrt{35}}{5}\vee x=\frac{7}{5}$$$$2.2x-5=0\vee \frac{3}{2}-x=1\Rightarrow x=\frac{5}{2}\vee x=\frac{1}{2}$$$$3.{\left(2^x\right)}^2-14\left(2^x\right)-32=0\Rightarrow 2^x=16\Rightarrow x=4$$

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