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How to solve this exponential equation:7*3^x+1-5^x+2=3^x+4-5^x+3  The answer is...

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edobro | Student, Grade 11 | Honors

Posted September 10, 2011 at 8:49 PM via web

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How to solve this exponential equation:7*3^x+1-5^x+2=3^x+4-5^x+3

 

The answer is supposed to be x=-1 but I'm not getting that.

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santaone | High School Teacher | eNoter

Posted September 11, 2011 at 9:47 AM (Answer #1)

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7*3^x+1-5^x+2=3^x+4-5^x+3

 

=> (7*3)3^x - 25*5^x = 81*3^x - 125*5^x

Taking everything to one side

=> (21-81) * 3 ^x +(-25+125)* 5 ^x = 0

=>100* 5 ^x = 60* 3 ^x

=> 5 * 5 ^x = 3* 3^x

=> 5^(x+1) = 3^(x +1)

taking log of both the sides

=> (x+1) log 5 = (x+1) log 3

 

But log 5 is not equal to log 3

 

Therefore x+1= 0

Therefore x=-1  ... Answer

 

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