Question

Prove that 3n-1 + 3n-1 3n+1 - 3n =2/3 ​

Answer 1

below

Explanation:

Step 1: Simplify the exponents

3n-1 × 3n+1 = 3(3n) × 3(3n) = 3^(2n) = 9^n

Step 2: Substitute the simplified expression back into the equation

3n-1 + 9^n - 3n = 2/3

Step 3: Combine like terms

(3n - 3n) + 9^n = 2/3

Step 4: Simplify further

0 + 9^n = 2/3

Step 5: Divide both sides by 9^n

9^n = 2/3

Step 6: Take the logarithm of both sides

n log 9 = log (2/3)

Step 7: Divide both sides by log 9

n = log (2/3) / log 9

Step 8: Use a calculator to find the numerical value of n

n ≈ -0.463