Question 1059802
Express the whole thing using base-two.   


{{{64=8^2=(2^3)^2=2^6}}}


{{{256=2^8}}}



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{{{4^(9x+3)=64/256}}}

{{{(2^2)^(9x+3)=(2^6)/(2^8)}}}

{{{2^(2(9x+3))=1/2^2}}}

{{{2^(18x+6)=2^(-2)}}}

You should understand, left and right members each are the base 2, raised to different expressioned exponents.  The exponents must be equal.  You can try taking logarithms-base two of both members, but you should understand through corresponding parts without the taking of logs....



{{{18x+6=-2}}}

{{{18x=-8}}}

{{{highlight(x=-4/9)}}}