Olympiad mathematics| Advanced Exponential Equation.

[@GillesF31]

Or this way to get the solution (step by step) ...
7^(x + 1) + 7^(x - 1) = 12

set k = x + 1

7^k + 7^(k - 2) = 12

7^x + 7^k/7^2 = 12

7^k + 7^k/49 = 12

49·7^k/49 + 7^k/49 = 12

50·7^k/49 = 12

50·7^k = 12·49

7^k = (12·49)/50

7^k = 11.76

recall: k = x + 1

7^(x + 1) = 11.76

7·7^x = 11.76

7^x = 11.76/7

7^x = 1.68

x = ln(1.68)/ln(7)

---

/// final result:

■ x = ln(1.68)/ln(7)

---

/// check:

7^(ln(1.68)/ln(7) + 1) + 7^(ln(1.68)/ln(7) - 1) = 12

🙂

[@dennismathacademy]

Nice Alternative

[@nasrullahhusnan2289]

[7^(x+1)]-[7^(x-1)]=12
7×(7^x)+(7^x)/7=12
(48/7)(7^x)=12
(4/7)(7^x)=1 --> 4[7^(x-1)]=1
7^(x-1)=¼
Take logarithm:
(x-1)log(7)=-log(4) --> x=1-⁷log(4) where ⁷log(4) is log based on 7

[@dennismathacademy]

👍

[@nasrullahhusnan2289]

Correction:
Line 3 must be (50/7)(7^x)=12
7^(x-1)=6/25
Then take logarithm