# Test: Logarithms I - Ambitious

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Question 1:   Find $x$, if $2{\mathrm{log}}_{7}\left(x\right)+{\mathrm{log}}_{7}\left(100\right)=2$
$x=1$
$x=±\frac{7}{10}$
$x=7$
$x=\frac{7}{10}$
Question 2:   Find $x$, if ${\mathrm{log}}_{3}^{2}\left(x\right)=4$
${x}_{1}=9,\text{\hspace{0.17em}}{x}_{2}=\frac{1}{9}$
$x=\frac{1}{9}$
$x=9$
${x}_{1}=4,\text{\hspace{0.17em}}{x}_{2}=\frac{1}{4}$
Question 3:   Find $x$, if ${\mathrm{log}}_{3}\left({x}^{2}-x-3\right)=1$
${x}_{1}=3,\text{\hspace{0.17em}}{x}_{2}=-2$
$x=-2$
$x=0$
$x=1$
Question 4:   Find $x$, if ${\mathrm{log}}_{\frac{1}{7}}\left({x}^{2}-6x+15\right)=-1$
$x=0$
${x}_{1}=2,\text{\hspace{0.17em}}{x}_{2}=4$
$x=2$
$x=1$
Question 5:   Find $x$, if ${\mathrm{log}}_{2}\left(\frac{x}{512}\right)×{\mathrm{log}}_{2}\left(x\right)=-20$
${x}_{1}=32,\text{\hspace{0.17em}}{x}_{2}=16$
$x=32$
$x=16$
${x}_{1}=16,\text{\hspace{0.17em}}{x}_{2}=8$
Question 6:   Calculate ${\mathrm{log}}_{2}\left(0.25\right)+{\mathrm{log}}_{2}\left(16\right)=...$
$4$
$1$
$\frac{1}{2}$
$2$
Question 7:   Calculate ${6}^{2{\mathrm{log}}_{6}\left(3\right)}+{\mathrm{log}}_{\frac{1}{3}}\left(9\right)=...$
$7$
$6$
$2$
$4$
Question 8:   Calculate ${4}^{{\mathrm{log}}_{2}\left(3\right)}+{10}^{2-\mathrm{log}\left(10\right)}+{2}^{{\mathrm{log}}_{4}\left(4\right)}=...$
$8$
$1$
$10$
$21$
Question 9:   Find $x$, if ${x}^{{\mathrm{log}}_{3}\left(9\right)}=4$
$x=2$
${x}_{1}=1,\text{\hspace{0.17em}}{x}_{2}=-1$
${x}_{1}=2,\text{\hspace{0.17em}}{x}_{2}=-2$
$x=3$
Question 10:   Calculate ${\mathrm{log}}_{13}\left(36\right)$, if ${\mathrm{log}}_{13}\left(3\right)=a,\text{\hspace{0.17em}}{\mathrm{log}}_{13}\left(2\right)=b$
$a+b$
${a}^{2}{b}^{2}$
$2a+2b$
$2a+b$