( ) EXAMPLE 5 Use inverse properties Simplify the expression. a.

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Presentation transcript:

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

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

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

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

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