Solve the simple exponential equation 2 (2x-3) - 2 (x-2) - 1= 0?

You do so by using the change-of-base formula. By the change-of-base formula, we see that: log?(x) = log?(x)/log?(4) = (1/2)log?(x). So the equation now becomes: log?(x + 1) - log?(x) = 1 log?(x + 1) - (1/2)log?(x) = 1 2log?(x + 1) - log?(x) = 2 log?(x + 1)²/x = 2 (x + 1)²/x = 4 x² + 2x + 1 = 4x x² - 2x + 1 = 0 (x - 1)² = 0 x = 1.

I hope this helps!

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