Exponent, Exponential and Logarithmic Equations
Exponent, Exponential and Logarithmic Equations
Solving Exponent Equations:
Ex: [pic]
1. multiply the exponent to its reciprocal (signs stay the same); what you do to one side of the equation you must do to the other side of the equation
[pic]
2. solve for x by plugging the values in the calculator
x = 8 ٨ (1/3)
x = 2
Solving Exponential Equations:
Ex: [pic]
1. If need, make the bases the same
[pic] [pic]
[pic]
2. Multiply the exponents if needed
[pic]
3. Ignore bases and set exponents equal to each other
[pic]
4. Solve for x:
[pic]
-2x -2x
2 = x
Rewriting exponents into logarithms:
LOG = EXPONENT
Ex: [pic]
1. Your exponent is your answer to the log problem.
Log = 2
2. The base is still the base just gets smaller.
[pic]
3. Whatever you didn’t use goes in the missing spot.
[pic]
Rewriting logarithms into exponents:
LOG = EXPONENT
Ex: [pic]
1. Whatever the log equals is your exponent.
Exponent is 2.
2. The base stays the same, just gets bigger.
Base is 2.
[pic]
3. Whatever you didn’t use is your answer.
[pic]
Solving logarithms:
Ex: [pic]
1. Rewrite log problem as an exponent problem
[pic]
2. Solve for x:
[pic]
[pic]
x = 8 ٨ (1/3)
x = 2
Logarithmic Rules:
Product Rule: [pic]
Quotient Rule: [pic]
Power Rule: [pic]
Solving logarithmic equations:
Ex: [pic]
1. Solve each log individually
[pic] [pic]
[pic] [pic]
[pic] [pic]
2. Replace logs with their values
[pic]
[pic]
3. Isolate the variable with the log
[pic]
-4 -4
[pic]
4. Solve log problem
[pic]
[pic]
Solving more complex ones:
Ex: [pic]
1. use any log laws possible
[pic]
2. Rewrite log into an exponent problem
[pic]
3. Solve for x:
[pic]
[pic]
(x – 5)(x + 2) = 0
x = 5, -2
4. Reject any negative answers
x = 5
Solving Exponential Equations where the bases cannot be the same:
Ex: [pic]
1. log both sides with the base of 10
[pic]
2. use any log laws needed
[pic]
3. solve for x:
[pic]
[pic]
[pic]
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