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EXAMPLE 5

log. log. log. a. b. 25 x. 10 log 4. 5. 5. 5. 4. a. 10 log 4. =. b. log x. = x. b. (. ). log. 25 x. b. =. 5 2. x. 5. 5 2 x. =. 2 x. =. b x. log. = x. b. EXAMPLE 5. Use inverse properties. Simplify the expression. SOLUTION.

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EXAMPLE 5

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  1. log log log a. b. 25x 10log4 5 5 5 4 a. 10log4 = b log x = x b ( ) log 25x b. = 52 x 5 52x = 2x = bx log = x b EXAMPLE 5 Use inverse properties Simplify the expression. SOLUTION Express 25 as a power with base 5. Power of a power property

  2. y = ln (x + 3) log a. b. y = 6 x 6 a. From the definition of logarithm, the inverse of is x. y = 6 y = x ex = (y + 3) ex – 3 y = ANSWER The inverse ofy =ln(x + 3) isy = ex – 3. EXAMPLE 6 Find inverse functions Find the inverse of the function. SOLUTION b. y = ln (x + 3) Write original function. x = ln (y + 3) Switch x and y. Write in exponential form. Solve for y.

  3. log log 10. 8 log x 8 7 7 8 x = b = x log x log b 8 b 7–3x 11. = x log ax –3x 7–3x = a for Examples 5 and 6 GUIDED PRACTICE Simplify the expression. SOLUTION SOLUTION

  4. log log log 12. 64x 2 2 2 log 64x = 2 26x = ( ) 26 x 6x = bx log = x b 13. eln20 e e 20 = = = x log x log 20 e e for Examples 5 and 6 GUIDED PRACTICE Simplify the expression. SOLUTION Express 64 as a power with base 2. Power of a power property SOLUTION eln20

  5. 14. Find the inverse of y = 4 x log 4 From the definition of logarithm, the inverse of y = x. y = 6 is 15. Find the inverse of y =ln(x – 5). ex = (y – 5) ex + 5 y = The inverse ofy =ln(x – 5) isy = ex + 5. ANSWER for Examples 5 and 6 GUIDED PRACTICE SOLUTION SOLUTION y =ln(x – 5) Write original function. x = ln (y – 5) Switch x and y. Write in exponential form. Solve for y.

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