Q. 24

Asked by Rayeesa | 10th Apr, 2018, 07:28: AM

Expert Answer:

begin mathsize 14px style 5 to the power of straight x plus 1 end exponent plus 5 to the power of 2 minus straight x end exponent equals 126
rightwards double arrow 5 to the power of straight x 5 plus 5 squared 5 to the power of negative straight x end exponent equals 126
Let space 5 to the power of straight x equals straight y
rightwards double arrow 5 straight y plus 25 cross times 1 over straight y equals 126
rightwards double arrow 5 straight y squared plus 25 equals 126 straight y
rightwards double arrow 5 straight y squared minus 126 straight y plus 25 equals 0
rightwards double arrow 5 straight y squared minus 125 straight y minus straight y plus 25 equals 0
rightwards double arrow 5 straight y left parenthesis straight y minus 25 right parenthesis minus 1 left parenthesis straight y minus 25 right parenthesis equals 0
rightwards double arrow left parenthesis straight y minus 25 right parenthesis left parenthesis 5 straight y minus 1 right parenthesis equals 0
rightwards double arrow straight y minus 25 equals 0 space or space 5 straight y minus 1 equals 0
rightwards double arrow straight y equals 25 space or space straight y equals 1 fifth
When space straight y equals 25 comma space
5 to the power of straight x equals 25 rightwards double arrow 5 to the power of straight x equals 5 squared rightwards double arrow straight x equals 2
When space straight y equals 1 fifth comma
5 to the power of straight x equals 1 fifth rightwards double arrow 5 to the power of straight x equals 5 to the power of negative 1 end exponent rightwards double arrow straight x equals negative 1

end style

Answered by Rashmi Khot | 10th Apr, 2018, 09:03: AM