We know that if two sides of an equation have the same base but different exponents, then the exponents must be equal. We use this idea to solve exponential equations by re-writing the expressions with the same base. In order to do that, we need to first think of some number to use as the base. Usually, multiple bases are possible (like 2, or 4, or even 1/2), but one might be easier than another. Be sure to re-write both sides as single terms (no + or -'s) before you eliminate the bases and work with the exponents only.
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