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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 rewriting 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 rewrite both sides as single terms (no + or 's) before you eliminate the bases and work with the exponents only.
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Sample Problems (6)
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Solving Exponential Equations with the 'Same' Base
Problem 1 8,318 viewsSolve:
7^{x − 1} = 49 
Solving Exponential Equations with the 'Same' Base
Problem 2 7,409 viewsSolve:
16^{x} = 8^{x − 1} 
Solving Exponential Equations with the 'Same' Base
Problem 3 6,568 viewsSolve:
( 1 )^{x} = 27² 9 
Solving Exponential Equations with the 'Same' Base
Problem 4 525 views 
Solving Exponential Equations with the 'Same' Base
Problem 5 511 views 
Solving Exponential Equations with the 'Same' Base
Problem 6 540 views
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