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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=53b−1=73−2cfinda⋅b⋅c=?

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=53b−1=73−2cThelastdigitof53b−1is1if3b−1=0or5if3b−1≠0Butthelastdigitof3a+2and73−2ccanno′tbe5.Theonlysolutionis3b−1=0then3a+2=53b−1=73−2c=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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