# Test: Logarithms II - Normal

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Question 1:   Find $x$, if ${\mathrm{log}}_{4}\left(5+3x\right)=3$
$x=\frac{29}{3}$
$x=1$
$x=5$
$x=\frac{59}{3}$
Question 2:   Find $x$, if ${\mathrm{log}}_{5}\left(2x+3\right)={\mathrm{log}}_{5}\left(x\right)$
$x=6$
$x=3$
$x=1$
$x=-3$
Question 3:   Compare logarithms based on the properties of the logarithmic function ${\mathrm{log}}_{\frac{1}{2}}\left(8\right)$ and ${\mathrm{log}}_{\frac{1}{2}}\left(512\right)$
Cannot be compared
They are equal
Question 4:   Find $x$, if ${\mathrm{log}}_{4}\left(x\right)=2$
$4$
$1$
$16$
$2$
Question 5:   Find the value of ${\mathrm{log}}_{2}26-{\mathrm{log}}_{2}13=...$
$4.6$
$5.7$
$4$
$1$
Question 6:   Find $x$, if ${\mathrm{log}}_{3}\left(7\right)+{\mathrm{log}}_{3}\left(2x\right)={\mathrm{log}}_{3}\left(112\right)$
$x=8$
$x=5$
$x=4$
$x=9$
Question 7:   Find $x$, if ${\mathrm{log}}_{5}\left(7-x\right)={\mathrm{log}}_{25}\left(9\right)$
$x=1$
$x=2$
$x=4$
$x=5$
Question 8:   Find $x$, if ${\mathrm{log}}_{x}\left(27\right)=3$
$x=9$
$x=3$
$x=6$
$x=27$
Question 9:   Find $x$, if ${\left(\frac{5}{6}\right)}^{x}=4$
$x={\mathrm{log}}_{\frac{5}{6}}\left(4\right)$
$x=\frac{5}{6}$
$x=7$
$x=1$
Question 10:   Compare logarithms based on the properties of the logarithmic function ${\mathrm{log}}_{\frac{9}{5}}\left(2\right)\text{\hspace{0.17em}}$ and ${\mathrm{log}}_{\frac{9}{5}}\left(4\right)$
They are equal
Cannot be compared