solution in terms of logarithm

label Algebra
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7^(3x-1)=6^(x-3)

need 1. solution set and 2. deciminal approx.

Jun 23rd, 2015

Thank you for the opportunity to help you with your question!

7^(3x-1)=6^(x-3)  =>  e^((3x-1)ln(7))  =  e^((x-3)ln(6))  =>  (3x-1)ln(7)=(x-3)ln(6)

so : 3ln(7)x - ln(7) = ln(6)x - 3ln(6) =>   x(3ln(7) - ln(6) ) = ln(7) - 3ln(6 )

so :  x = (ln(7) - 3ln(6 )) / (3ln(7) - ln(6)) = ln(7 / 216) / ln(343 / 6)

so  the solution set is :  {ln(7 / 216) / ln(343 / 6)}

the approx :  x = - 0,847598


Good Luck 

my friend

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 23rd, 2015

is it 216 over 7?

Jun 23rd, 2015

we have  3ln(6) = ln(6^3) =  ln(216) 

and :  3ln(7) = ln(7^3) = ln(343) 

and we now : ln(a) - ln(b) = ln(a / b) 

so : ln(7) - ln(216)= ln(7 / 216 )

and : ln(343) - ln(6) =  ln(343 / 6) 

Good lUck 

and if you dont understaind let me know where is the trouble 

Jun 23rd, 2015

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