Japanese Math Olympiad Exponential Equations | Math Olympiad Strategies Revealed"

[@ManojkantSamal]

X={log7 with base (8/7)}-7.....May be

[@mariapham4669]

Xlog8/7=log7/8^7*7=log7/8^7+log7=log7-7log8/7=>x=log7/log8/7-7=1/[log78-1]-7

[@Sergey_Moskvichev]

(7/8)ˣ=8⁷/7⁸=8⁷/(7⁷×7)=(8/7)⁷×1/7=(7/8)⁻⁷×1/7.
Прологарифмируйте по основанию 7/8 получите
x=log(1/7)-7.
Такой ответ красивый.

[@wes9627]

(x+8)ln7=(x+7)ln8; (ln8-ln7)x=8ln7-7ln8; x=(8ln7-7ln8)/(ln8-ln7)

[@GillesF31]

Yes, or ...
7^(x + 8) = 8^(x + 7)

7^x·7^8 = 8^x·8^7

7^8 = (8^x/7^x)·8^7

8^x/7^x = 7^8/8^7

(8/7)^x = 7^8/8^7

x = log(7^8/8^7)/log(8/7)

■ x = 7.572679
🙂