2 To obtain an accurate spectrophotometric measurement of the glucose concentration in the sample water is added to dissolve the glucose. barium hydroxide is added to prevent blood clots. an enzymatic color reagent is added that digests and, thus, removes blood clots. heparin is added to prevent blood clots.

Write an equivalent logarithmic equation for the following exponential equations and solve for \( x \). Leave your answers in logarithmic form. a. \( 4^{x}=8 \) \( x=\square \) b. \( 2^{x}=3 \) \( x=\square \) c. \( 5^{x}=5 \) \( x=\square \)

The function \( f(x)=2^{x+1} \) is graphed below. Use the reflection about the line \( y=x \) to graph the inverse function \( y=f^{-1}(x) \) on the same plane. First place a point on the asymptote and then plot two points on the curve.

Find the fraction of a circle that encloses the given angle. \( \begin{array}{ll}\text { 3) } 6^{\circ} & \text { 4) } 24^{\circ}\end{array} \)

29. Let \[ A=\left[\begin{array}{rrrr}1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & -1 & 1 & 1\end{array}\right] \] We wish to determine all \( 4 \times 3 \) matrices \( X \) for which \( A X A=A \) Observe that \[ P A Q=\left[\begin{array}{rrrr}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right] \] where \( P \) and \( Q \) are the invertible matrices \[ P=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ -1 & 2 & 1\end{array}\right] \text { and } Q=\left[\begin{array}{rrrr}1 & -1 & -1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 1\end{array}\right] \] (a) Explain how you can use this to convert the problem of finding all \( X \) so that \( A X A=A \) to finding all \( 4 \times 3 \) matrices \( Y \) so that \( B Y B=B \), where \( B=P A Q \). Make sure to indicate how \( X \) and \( Y \) are related. (b) Find all \( Y \) so that \( B Y B=B \). (c) Use your answer in (b) to find all \( X \) so that \( A X A=A \). (d) Give 2 explicit \( X \) with \( A X A=A \).

Salah satu akar persamaan kuadrat \( x^{2}-(2 a- \) 6) \( x+3=0 \) adalah tiga kali akar yang lain. Penjumlahan dari nilai-nilai a yang memenuhi persamaan tersebut adalah...