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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 🙂
Nice Alternative
[7^(x+1)]-[7^(x-1)]=127×(7^x)+(7^x)/7=12(48/7)(7^x)=12(4/7)(7^x)=1 --> 4[7^(x-1)]=1 7^(x-1)=¼Take logarithm:(x-1)log(7)=-log(4) --> x=1-⁷log(4) where ⁷log(4) is log based on 7
👍
Correction:Line 3 must be (50/7)(7^x)=127^(x-1)=6/25Then take logarithm
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
🙂
Nice Alternative
[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
👍
Correction:
Line 3 must be (50/7)(7^x)=12
7^(x-1)=6/25
Then take logarithm