Quadratic Equations
New Zealand
Level 7 - NCEA Level 2
Logs and power functions reducible to quadratics
Interactive practice questions
Consider the equation
$\left(2^x\right)^2-9\times2^x+8=0$(2x)2−9×2x+8=0
a
The equation can be reduced to a quadratic equation by using a certain substitution.
By filling in the gaps, determine the correct substitution that would reduce the equation to a quadratic.
Let $m=\left(\editable{}\right)^{\editable{}}$m=()
b
Solve the equation for $x$x by using the substitution $m=2^x$m=2x.
Easy
3min
Solve the following equation for $x$x by substituting in $m=4^x$m=4x.
$4^{2x}-65\times4^x+64=0$42x−65×4x+64=0
Use a comma to separate multiple solutions.
Easy
2min
Solve for $x$x:
$2^{2x}-12\times2^x+32=0$22x−12×2x+32=0
Let $p=2^x$p=2x.
Easy
2min
Solve for $x$x:
$4\times2^{2x}-34\times2^x+16=0$4×22x−34×2x+16=0
Easy
4min
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