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Solve each equation 1) log5-log2x=1 2) 2log(x+1)=5

User Cystbear
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1 Answer

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1)\\log5-log2x=1;\ D:x > 0\\\\log(5:2x)=log10\\\\log(5)/(2x)=log10\iff(5)/(2x)=10\\\\20x=5\ \ \ /:20\\\\x=(1)/(4)\in D



2)\\2log(x+1)=5;\ D:x+1 > 0\to x > -1\\\\log(x+1)^2=log10^5\iff(x+1)^2=10^5\\\\x+1=-√(10^5)\ \vee\ x+1=√(10^5)\\\\x+1=-√(10^4\cdot10)\ \vee\ x+1=√(10^4\cdot10)\\\\x=-100√(10)-1\\otin D\ \vee\ x=100√(10)-1\in D
User Rfsbraz
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