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if-3-a-2-5-3b-1-7-3-2c-find-a-b-c-




Question Number 147231 by mathdanisur last updated on 19/Jul/21
if   3^(a+2)  = 5^(3b−1)  = 7^(3−2c)   find   a∙b∙c = ?
if3a+2=53b1=732cfindabc=?
Answered by Olaf_Thorendsen last updated on 19/Jul/21
3^(a+2)  = 5^(3b−1)  = 7^(3−2c)     The last digit of 5^(3b−1)  is 1 if 3b−1 = 0  or 5 if 3b−1 ≠ 0    But the last digit of 3^(a+2)   and 7^(3−2c)   canno′t be 5.    The only solution is 3b−1 = 0 then  3^(a+2)  = 5^(3b−1)  = 7^(3−2c)  = 1 and  a = −2, b = (1/3), c = (3/2)    abc = −2×(1/3)×(3/2) = −1
3a+2=53b1=732cThelastdigitof53b1is1if3b1=0or5if3b10Butthelastdigitof3a+2and732ccannotbe5.Theonlysolutionis3b1=0then3a+2=53b1=732c=1anda=2,b=13,c=32abc=2×13×32=1
Commented by mathdanisur last updated on 19/Jul/21
cool Ser thank you
coolSerthankyou

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