Question 249342
{{{ 4^(x-4)=0.5^(5-2x) }}} Start with the given equation.



{{{ (2^2)^(x-4)=(1/2)^(5-2x) }}} Rewrite {{{4}}} as {{{2^2}}}. Rewrite {{{0.5}}} as {{{1/2}}}



{{{ (2^2)^(x-4)=(2^(-1))^(5-2x) }}} Rewrite {{{1/2}}} as {{{2^(-1)}}}
 


{{{ 2^(2(x-4)) =2^(-(5-2x)) }}} Multiply the exponents.



{{{2(x-4)=-(5-2x)}}} Since the bases are equal, the exponents are equal.



{{{2x-8=-5+2x}}} Distribute.



{{{2x=-5+2x+8}}} Add {{{8}}} to both sides.



{{{2x-2x=-5+8}}} Subtract {{{2x}}} from both sides.



{{{0x=-5+8}}} Combine like terms on the left side.



{{{0x=3}}} Combine like terms on the right side.



{{{0=3}}} Simplify.



Since this equation is <font size=4><b>never</b></font> true for any x value, this means that there are no solutions.



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Answer:


So there are no solutions to the equation {{{ 4^(x-4)=0.5^(5-2x) }}}