##### solution in terms of logarithm

 Algebra Tutor: None Selected Time limit: 1 Day

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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Jun 23rd, 2015
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Jun 23rd, 2015
May 24th, 2017
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