clara1223
  • clara1223
solve for x: 4^(-x-3)+3=35 a) x=15/2 b) x=-8 c) x=-1/2 d) x=11/2 e) x=-11/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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clara1223
  • clara1223
\[4^{-x-3}+3=35\]
DecentNabeel
  • DecentNabeel
\[4^{\left(-x-3\right)}+3=35\quad :\quad x=-\frac{11}{2}\]
DecentNabeel
  • DecentNabeel
answer is option e

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clara1223
  • clara1223
@DecentNabeel please explain
DecentNabeel
  • DecentNabeel
ok 4^(-x-3)+3=35 first subtract 3 on both sides
DecentNabeel
  • DecentNabeel
4^(-x-3)+3-3=35-3 4^(-x-3)=32
DecentNabeel
  • DecentNabeel
\[\left(2^2\right)^{-x-3}=2^5\] \[\left(2^2\right)^{-x-3}=2^5\] \[\mathrm{Use\:the\:following\:exponent\:property}:\quad \left(a^n\right)^m=a^{n\cdot m}\] \[\left(2^2\right)^{-x-3}=2^{2\left(-x-3\right)}\] \[2^{2\left(-x-3\right)}=2^5\] \[\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)\] \[\mathrm{Solve\:}\:2\left(-x-3\right)=5:\quad x=-\frac{11}{2}\]
DecentNabeel
  • DecentNabeel
are you understand @clara1223
clara1223
  • clara1223
yes! thanks so much @DecentNabeel
DecentNabeel
  • DecentNabeel
you are wellcome @clara1223

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