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L e t space f colon A rightwards arrow B space d e f i n e d space a s space f open parentheses x close parentheses equals a to the power of x comma space a greater than 0 comma space x element of R space a n d space a not equal to 1 comma space t h e n space d e f i n e space t h e space s e t space B.

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Asked by Topperlearning User 25th October 2016, 9:02 AM
Answered by Expert
Answer:

L e t space f colon A rightwards arrow B space d e f i n e d space a s space f open parentheses x close parentheses equals a to the power of x comma space a greater than 0 comma space x element of R space a n d space a not equal to 1.
rightwards double arrow y equals a to the power of x
T a k i n g space log space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma
log y equals log a to the power of x
rightwards double arrow l o g y equals x l o g a
rightwards double arrow x equals fraction numerator log y over denominator log a end fraction
F o r space x space t o space b e space r e a l comma space y space s h o u l d space b e space p o s i t i v e.
rightwards double arrow y greater than 0
rightwards double arrow y element of R to the power of plus
T h u s comma space t h e space s e t space B space i s space R to the power of plus.

Answered by Expert 25th October 2016, 11:02 AM
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