9514 1404 393
Answer:
x = -2 or 3
Step-by-step explanation:
Let z = 2^x. Then the equation becomes ...
[tex]2^{2x+2}+8=33(2^x)\\\\(2^2)(2^x)^2+8=33(2^x)\\\\4z^2+8=33z \qquad\text{substitute $z$ for $2^x$}\\\\4z^2-33z+8=0 \qquad\text{put the quadratic in standard form}\\\\(4z-1)(z-8)=0 \qquad\text{factor}\\\\z=\dfrac{1}{4}\text{ or }z=8\qquad\text{values of z that make the factors 0}\\\\x=\log_2{z}=\{-2,\ 3\}[/tex]
The values of x that satisfy the equation are -2 and 3.
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For the graph, we rewrite the equation to the form ...
f(x) = 0
where
f(x) = 2^(2x+2) +8 -33(2^x)
Then the x-intercepts of the function are the solution values for x.
