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6^(n+7)=7^(n+6)ln(6^(n+7))=ln(7^(n+6))(n+7)ln6=(n+6)ln7n(ln6-ln7)=6ln7-7ln6n=(6ln7-7ln6)/(ln6-ln7)
3^3^n3^4 3^4^n^3^3 1^1^n^1^2^2 1^2^2^n+1^3 n^1^1 1^2^n+3^1 2^n+3 (n ➖ 3n+2).
Here’s a better solution:7^(n+6)=6^(n+7)7^(n+6)=6^(n+6)6(7/6)^(n+6)=6n+6=log(6, 7/6)n=log(6, 7/6)-6
When you calculate the answer with a calculator you don't get a "more precise answer!" In fact, you get a less precise answer! Nonetheless it's interesting what the numerical, approximate answer is but I am too lazy to do it myself.
6^(n+7)=7^(n+6)
ln(6^(n+7))=ln(7^(n+6))
(n+7)ln6=(n+6)ln7
n(ln6-ln7)=6ln7-7ln6
n=(6ln7-7ln6)/(ln6-ln7)
3^3^n3^4 3^4^n^3^3 1^1^n^1^2^2 1^2^2^n+1^3 n^1^1 1^2^n+3^1 2^n+3 (n ➖ 3n+2).
Here’s a better solution:
7^(n+6)=6^(n+7)
7^(n+6)=6^(n+6)6
(7/6)^(n+6)=6
n+6=log(6, 7/6)
n=log(6, 7/6)-6
When you calculate the answer with a calculator you don't get a "more precise answer!" In fact, you get a less precise answer! Nonetheless it's interesting what the numerical, approximate answer is but I am too lazy to do it myself.