Wiskundeleraar

extra opgaven uitgewerkt

$
\begin{array}{l}
y = 25 - 5^{\frac{1}{2}x + 2} \\
y - 25 = - 5^{\frac{1}{2}x + 2} \\
- y + 25 = 5^{\frac{1}{2}x + 2} \\
\frac{1}{2}x + 2 = {}^5\log \left( { - y + 25} \right) \\
\frac{1}{2}x = {}^5\log \left( { - y + 25} \right) - 2 \\
x = 2 \cdot {}^5\log \left( { - y + 25} \right) - 4 \\
\end{array}
$

$
\begin{array}{l}
y = 3 \cdot 2^x + 5 \\
3 \cdot 2^x = y - 5 \\
2^x = \frac{1}{3}y - 1\frac{2}{3} \\
x = {}^2\log \left( {\frac{1}{3}y - 1\frac{2}{3}} \right) \\
\end{array}
$

of...

$
\begin{array}{l}
y = 3 \cdot 2^x + 5 \\
3 \cdot 2^x = y - 5 \\
2^x = \frac{{y - 5}}{3} \\
x = {}^2\log \left( {\frac{{y - 5}}{3}} \right) \\
\end{array}
$

$ \begin{array}{l} y = 10^{x^2 } - 1 \\ 10^{x^2 } = y + 1 \\ x^2 = \log (y + 1) \\ x = \sqrt {\log (y + 1)} \\ \end{array} $

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