If 22n + 22n + 22n + 22n = 424, then n =
4 to the power of 24
The left side of the equation has 22n added to itself four times, so just rewrite as 422n:
Next it will help to get the bases to all be the same. Rewrite the 4 as 22, the 22n is fine, and rewrite the 4 on the right side of the equation as 22:
Finally, combine the 2's on the left side. Remember that when we multiply two numbers we add the exponents:
If the bases are the same and they're on either side of an equals sign, then the exponents must be equal too! We can focus on the exponents only and solve for n:
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