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Opgave 1
a. $ \eqalign{   & {}^3\log \left( {2x^2  - 3} \right) = 6  \cr   & 2x^2  - 3 = 3^6   \cr   & 2x^2  - 3 = 729  \cr   & 2x^2  = 732  \cr   & x^2  = 366  \cr   & x =  - \sqrt {366} \,\,of\,\,x = \sqrt {366}  \cr} $	b. $ \eqalign{   & {}^{\frac{1} {2}}\log \left( {\frac{1} {{4x}}} \right) = 4  \cr   & \frac{1} {{4x}} = \left( {\frac{1} {2}} \right)^4   \cr   & \frac{1} {{4x}} = \frac{1} {{16}}  \cr   & 4x = 16  \cr   & x = 4 \cr} $	c. $ \eqalign{   & {}^2\log \left( {4 - 30x^2 } \right) =  - 2  \cr   & 4 - 30x^2  = 2^{ - 2}   \cr   & 4 - 30x^2  = \frac{1} {4}  \cr   & 16 - 120x^2  = 1  \cr   & 120x^2  = 15  \cr   & x^2  = \frac{1} {8}  \cr   & x =  - \sqrt {\frac{1} {8}} \,\,of\,\,x = \sqrt {\frac{1} {8}}   \cr   & x =  - \frac{1} {4}\sqrt 2 \,\,of\,\,x = \frac{1} {4}\sqrt 2  \cr} $

Opgave 2
$3^{x+1}=80$ $x+1=^3log(80)$ $x=-1+^3log(80)$	$5+2^{3x}=25$ $2^{3x}=20$ $3x=^2log(20)$ $x=\frac{1}{3}·^2log(20)$	$\eqalign{4-log(\frac{1}{x})=2}$ $\eqalign{-log(\frac{1}{x})=-2}$ $\eqalign{log(\frac{1}{x})=2}$ $\eqalign{\frac{1}{x}=100}$ $\eqalign{x=\frac{1}{100}}$

Opgave 3
$ \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} $