How to Solve Exponential Equations

Step-by-Step Guide

1. 1

   Step 1: Determine whether the two exponents have the same base.

   The base is the big number in an exponential expression.You can only use this method when you are presented with an equation that has an exponent on either side, and each exponent has the same base.
   
   For example, 65+y=63{\displaystyle 6^{5+y}=6^{3}} has an exponent on either side of the equation, and each exponent has the same base (6).
2. 2

   Step 2: Ignore the base.

   Since the exponents are equal and have the same base, their exponents must be equal.
   
   As such, you can ignore the base and write an equation for the exponents only.For example, in the equation 65+y=63{\displaystyle 6^{5+y}=6^{3}}, since both exponents have the same base, you would write an equation for the exponents: 5+y=3{\displaystyle 5+y=3}. , To do this, you need to isolate the variable.
   
   Remember that whatever you do to one side of an equation, you must do to the other side of the equation.
   
   For example:5+y=3{\displaystyle 5+y=3}5+y−5=3−5{\displaystyle 5+y-5=3-5}y=−2{\displaystyle y=-2} , To make sure that your answer is correct, plug the value you found for the variable back into the original equation, and simplify the expression.
   
   The two sides should be equal.
   
   For example, if you found that y=−2{\displaystyle y=-2}, you would substitute −2{\displaystyle
   -2} for y{\displaystyle y} in the original equation:65+y=63{\displaystyle 6^{5+y}=6^{3}}65−2=63{\displaystyle 6^{5-2}=6^{3}}63=63{\displaystyle 6^{3}=6^{3}}
3. 3

   Step 3: Solve the equation.

4. 4

   Step 4: Check your work.

Detailed Guide

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