Solving Exponential Equations

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Presentation transcript:

Solving Exponential Equations I. Relationship between Exponential and Logarithmic Equations. A) Logs and Exponentials are INVERSES of each other. 1) That means they cancel each other out. B) To solve equations that have a variable in the exponent, you convert them into logarithmic form. C) To solve equations that have a logarithm in them, you convert them into exponential form. D) Remember that ln is loge. You might have to rewrite it in its other form to solve for x.

Solving Exponential Equations II. Solving Exponential Equations Using Logarithmic Inverse. A) Circle the part that has the exponent ( bx ). B) Isolate the circled part. 1) Basic algebra solving. 2) Now you have baseexpo = #. C) Convert it into logarithmic form. 1) log base # = exponent. D) Evaluate using a calculator log base # = E) Solve for the variable (if needed).

Solving Exponential Equations Examples: Solve for the variable. 1). 2 (5)3x – 8 = 10 2 (5)3x – 8 = 10 (circle the expo part) 2 (5)3x = 18 (isolate the circled part) (Add 8) (5)3x = 9 ( ÷ by 2 ) log 5 9 = 3x (convert into log form) = 1.365 = 3x (evaluate with a calculator) .455 = x ( solve for x) (÷ by 3 )

Solving Exponential Equations ½ (3)2x–5 + 7 = 21 (circle the expo part) ½ (3)2x–5 = 14 (isolate circled part) (subtract 7) (3)2x–5 = 28 ( multiply by 2 ) log 3 28 = 2x – 5 (convert into log form) = 3.033 = 2x – 5 (evaluate with calculator) 8.033 = 2x ( solve for x) ( add 5 ) 4.017 = x ( ÷ by 2 )