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Question Number 190686 by Yacouba last updated on 09/Apr/23

$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}x$$$$e^{\ln (2x+5)}=\ln e(8x+3)$$

Answered by aba last updated on 09/Apr/23

$${\mathrm{e}}^{\ln (2\mathrm{x}+5)}=\ln \left({\mathrm{e}}^{8\mathrm{x}+3}\right)\Rightarrow 2\mathrm{x}+5=8\mathrm{x}+3\Rightarrow \mathrm{x}=\frac{1}{3}$$

Answered by Humble last updated on 09/Apr/23

$$\mathrm{by}\mathrm{exponential}\mathrm{rule},\mathrm{the}\mathrm{above}\mathrm{is}$$$$2\mathrm{x}+5=8\mathrm{x}+3$$$$2\mathrm{x}-8\mathrm{x}=3-5$$$$-6\mathrm{x}=-2$$$$\mathrm{x}=\frac{-2}{-6}$$$$\mathrm{x}=\frac{1}{3}$$

Commented by AROUNAMoussa last updated on 10/Apr/23

C'est cool !

Commented by heavenlyfreedom last updated on 12/Apr/23

$$wrong,lne(8x+5)=lne+ln(8x+3)$$$$=1+ln(8x+3)$$

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