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Question Number 167800 by cortano1 last updated on 25/Mar/22

$$5^{2x}=2.{10}^x-4^{2x}$$$$\sqrt[{(x+2)}^{-1}]{{(x-4)}^{x^2+2}}=?$$

Commented by MJS_new last updated on 25/Mar/22

$$x=0$$

Commented by logan whetzel last updated on 26/Mar/22

please explain this awnser

Commented by MJS_new last updated on 26/Mar/22

$$5^{2x}+4^{2x}=2\times {10}^x$$$${25}^x+{16}^x=2\times {10}^x$$$$\left(1\right)x=0$$$${25}^0+{16}^0=2\times {10}^0$$$$1+1=2\times 1\mathrm{true}$$$$\left(2\right)x=-\mathrm{\infty }$$$${25}^{-\mathrm{\infty }}+{16}^{-\mathrm{\infty }}=2\times {10}^{-\mathrm{\infty }}$$$$0+0=2\times 0\mathrm{true}$$$$$$$$\mathrm{no}\mathrm{other}\mathrm{solution}$$

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