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Question Number 50698 by Cheyboy last updated on 19/Dec/18

$$\mathrm{Solve}\mathrm{for}\mathrm{x}$$$$$$$$4^{2\mathrm{x}+1}\times 5^{\mathrm{x}-2}=6^{1-\mathrm{x}}$$

Answered by MJS last updated on 19/Dec/18

$$(2x+1)\ln 4+(x-2)\ln 5=(1-x)\ln 6$$$$(2\ln 4+\ln 5+\ln 6)x=\ln 6-\ln 4+2\ln 5$$$$(5\ln 2+\ln 3+\ln 5)x=-\ln 2+\ln 3+2\ln 5$$$$x=\frac{-\ln 2+\ln 3+2\ln 5}{5\ln 2+\ln 3+\ln 5}\approx .587053$$

Commented by Cheyboy last updated on 19/Dec/18

$$\mathrm{Thank}\mathrm{you}\mathrm{Sir}\mathrm{Godblesd}\mathrm{you}$$$$$$

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