[tex]\bold{\blue{\dfrac{2^{x}+(22)^{x}+(222)^{x}}{3^{x}+(33)^{x}+(333)^{x}}=\dfrac{9}{4}} }[/tex]
[tex]\bold{\pink{\dfrac{2^{x}+(22)^{x}+(222)^{x}}{3^{x}+(33)^{x}+(333)^{x}}=[\dfrac{4}{9}]^{-1} }}[/tex]
[tex]\bold{\green{\dfrac{2^{x}(1+11^{x}+111^{x})}{3^{x}(1+11^{x}+111^{x})}=((\dfrac{2}{3})^{{{2}}})^{{{-1}}} }}[/tex]
[tex]\bold{\orange{\dfrac{2^{x}\cancel{(1+11^{x}+111^{x})}}{3^{x}\cancel{(1+11^{x}+111^{x})}}=(\dfrac{2}{3})^{-2} }}[/tex]
[tex]\bold{\purple{\dfrac{2^{x}}{3^{x}}=(\dfrac{2}{3})^{-2} }}[/tex]
[tex]\bold{\red{(\dfrac{2}{3})^{x} =(\dfrac{2}{3})^{-2} }}[/tex]
[tex]\bold{\green{ x=-2 } }[/tex]
Answer:
Step-by-step explanation:
simplify upper n lower fraction of LHS:
2^x+22^x+222^x
= 2^x*1 + (2*11)^x + (2*111)^x
= 2^x*1 + 2^x*11^x + 2^x*111^x
= 2^x*(1+11^x+111^x)
3^x+33^x+333^x
= 3^x*1 + (3*11)^x + (3*111)^x
= 3^x*1 + 3^x*11^x + 3^x*111^x
= 3^x*(1+11^x+111^x)
so LHS
= 2^x*(1+11^x+111^x) / (3^x*(1+11^x+111^x))
= 2^x / 3^x
= (2/3)^x
RHS = 9/4
= (3^2/ 2^2)
= (3/2)^2
= (2/3)^(-2)
so x = -2
