EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base 2. 1 2 Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

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

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 = ? 1 2 – 2– 2 1 – 31 – 3 1 ? = 4

GUIDED PRACTICE for Example 1 Solve the equation = 27 2x2x x – 1 9 = 27 2x2x x – 1 SOLUTION (3 ) = (3 ) 2 x – 12x2x 3 3 = 3 4x4x3x – 3 Rewrite 9 and 27 as powers with base 3. Write original equation. Power of a power property 4x = 3x –3 Property of equality for exponential equations 9 = 27 2x2x 9 = (9 3) 2x2x x – 1

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

GUIDED PRACTICE for Example 1 Solve the equation = x + 1 3x – 2 SOLUTION (10 ) = (10 ) 2 3x – 27x+1 3 Rewrite 100 and 1000 as powers with base 10. Write original equation. Power of a power property 14x + 2 = 9x – 6 Property of equality for exponential equations 100 = x + 1 3x – 2 (10 ) = (10 ) 9x – 6 14x+2

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

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

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