solve the following question : if 3 raise to power a = 5 raise to power -b = 15 raise to power c, then prove that : 1/a - 1/b - 1/c = 0

Asked by Vikas | 22nd May, 2017, 12:16: AM

Expert Answer:

begin mathsize 16px style Let space 3 to the power of straight a equals 5 to the power of negative straight b end exponent equals 15 to the power of straight c equals straight k
rightwards double arrow 3 to the power of straight a equals straight k rightwards double arrow 3 equals straight k to the power of 1 over straight a end exponent

5 to the power of negative straight b end exponent equals straight k rightwards double arrow 5 equals straight k to the power of negative 1 over straight b end exponent
15 to the power of straight c equals straight k rightwards double arrow 15 equals straight k to the power of 1 over straight c end exponent
rightwards double arrow 3 cross times 5 equals straight k to the power of 1 over straight c end exponent
rightwards double arrow straight k to the power of 1 over straight a end exponent cross times straight k to the power of negative 1 over straight b end exponent equals straight k to the power of 1 over straight c end exponent
rightwards double arrow straight k to the power of 1 over straight a minus 1 over straight b end exponent equals straight k to the power of 1 over straight c end exponent
rightwards double arrow 1 over straight a minus 1 over straight b equals 1 over straight c end style

Answered by Rashmi Khot | 22nd May, 2017, 03:23: PM