A Very Nice Exponential Equation

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[@RAG981]

I got a= ln((rt5+1)/2)/ln(9/2) by sorting the original equation into powers of 2 and 3, then treating as a quadratic in 3^2a. This gave 3^2a = 2^a((1+rt5)/2), and then taking logs and collecting "a" terms gave the answer. Nice.

[@elmer6123]

Step 1. Learn to recognize that problems like this are associated with the Golden Ratio, the positive root of Φ^2-Φ-1=0 or φ^2+φ-1=0.
Step 2. Divide the given equation by one of its terms and rearrange the results into one of these two forms.
Step 3. Note that Φ=(√5+1)/2, φ=(√5-1)/2, and Φφ=Φ-φ=1.
Step 4. Try associating the given equation with each of these two forms and see why some use (√5+1)/2 and others use (√5-1)/2.

[@barakathaider6333]

👍

[@yakupbuyankara5903]

a=log(2/9)^((5^(1/2)-1)/2)