Question 1054651
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If 4^(x-1)=9, find the values of 2^x and 8^-x
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If {{{4^(x-1)}}} = 9,  then  {{{(1/4)*4^x}}} = 9.


Then {{{4^x}}} = 36,  or  {{{2^(2x)}}} = 36,   or  {{{(2^x)^2}}} = 36.


Then {{{2^x}}} = {{{sqrt(36)}}}  and,  hence,  {{{2^x)}}} = 6.


Having this, we can write {{{8^(-x)}}} = {{{2^(-3x)}}} = {{{(2^x)^(-3)}}} = {{{6^(-3)}}} = {{{1/216}}}.
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All questions are answered.