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Question Number 170203 by bounhome last updated on 18/May/22

$$solve:5^{lgx}=50-x^{lg5}$$

Answered by aleks041103 last updated on 18/May/22

$$5^{lgx}={10}^{\left(lgx\right)\left(lg5\right)}=y$$$$x^{lg5}={10}^{\left(lgx\right)\left(lg5\right)}=y$$$$\Rightarrow 2y=50$$$$\Rightarrow y=5^{lgx}=25$$$$\Rightarrow lgx=2\Rightarrow x={10}^2=100$$$$\Rightarrow x=100$$

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