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

need 1. solution set and 2. deciminal approx.

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

is it 216 over 7?

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

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