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Question
Solve the following equation.
3+2logx+13=2log3(x+1)
3+2logx+13=2log3(x+1)
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Solution
3+2logx+13=2log3x+1
Let log3x+1=a
Therefore, 3+2a=2a2a2−3a−2=0⇒2a2−4a+a−2=0⇒(2a+1)(a−2)=0⇒a=−12,2
Therefore, log3x+1=−12,log3x+1=2⇒x+1=1√3,9⇒x=1−√3√3,8.
3+2logx+13=2log3x+1
Let log3x+1=a
Therefore, 3+2a=2a2a2−3a−2=0⇒2a2−4a+a−2=0⇒(2a+1)(a−2)=0⇒a=−12,2
Therefore, log3x+1=−12,log3x+1=2⇒x+1=1√3,9⇒x=1−√3√3,8.
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