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EXAMPLE 1

1. x – 3. x. 2. Solve 4 =. x – 3. 2 x. – x + 3. x. 2 = 2. 1. 1. 4 =. Rewrite 4 and as powers with base 2. 2. 2. x. x – 3. 2. – 1. (2 ) = (2 ). ANSWER. The solution is 1. EXAMPLE 1. Solve by equating exponents. SOLUTION. Write original equation.

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EXAMPLE 1

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  1. 1 x –3 x 2 Solve 4= x –3 2 x – x +3 x 2 = 2 1 1 4= Rewrite 4 and as powers with base 2. 2 2 x x –3 2 –1 (2 ) = (2 ) ANSWER The solution is 1. EXAMPLE 1 Solve by equating exponents SOLUTION Write original equation. Power of a power property Property of equality for exponential equations 2x = – x + 3 x = 1 Solve for x.

  2. –2 ? 4 = 1 1 2 2 1–3 ? 1 4 = EXAMPLE 1 Solve by equating exponents Check: Check the solution by substituting it into the original equation. Substitute 1 for x. Simplify. Solution checks. 4 = 4

  3. x –1 2x 9 = 27 x –1 2x 9 = (9•3) 2x x –1 2 3 (3 ) = (3 ) x –1 2x 1. 9 = 27 4x 3x –3 3 = 3 for Example 1 GUIDED PRACTICE Solve the equation. 2x 9 = 27 SOLUTION Write original equation. Rewrite 9and 27 as powers with base 3. Power of a power property 4x = 3x –3 Property of equality for exponential equations

  4. ANSWER The solution is – 3. for Example 1 GUIDED PRACTICE 4x – 3x =–3 Property of equality for exponential equations =–3 Solve for x.

  5. 3x –2 7x +1 100 = 1000 7x+1 3x –2 2 3 (10 ) = (10 ) 14x+2 9x –6 (10 ) = (10 ) 7x +1 3x –2 2. 100 = 1000 for Example 1 GUIDED PRACTICE Solve the equation. SOLUTION Write original equation. Rewrite 100and 1000 as powers with base 10. Power of a power property 14x + 2 = 9x – 6 Property of equality for exponential equations

  6. x = – 8 – 8 5 5 ANSWER The solution is . for Example 1 GUIDED PRACTICE 14x – 9x =– 6 – 2 Property of equality for exponential equations 5x = – 8 Property of equality for exponential equations Solve for x.

  7. 5x –6 3 – x 81 = 1 1 3 – x 5x –6 4 –1 (3 ) = (3 ) 3 3 5x –6 3 – x 3. 81 = 12–4x –5x+6 3 = 3 for Example 1 GUIDED PRACTICE Solve the equation. SOLUTION Write original equation. Rewrite 81 and 1/3 as powers with base 3. Power of a power property Property of equality for exponential equations 12–4x = –5x+6

  8. ANSWER The solution is – 6 . for Example 1 GUIDED PRACTICE – 4x + 5x = 6 – 12 Property of equality for exponential equations x =– 6 Solve for x.

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