# Test: Logarithms I - Normal

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Question 1:   Compare logarithms based on the properties of the logarithmic function ${\mathrm{log}}_{\frac{5}{2}}\left(3\right)$ and ${\mathrm{log}}_{\frac{5}{2}}\left(9\right)$
Cannot be compared
They are equal
Question 2:   Compare logarithms based on the properties of the logarithmic function ${\mathrm{log}}_{\frac{1}{7}}\left(5\right)$ and ${\mathrm{log}}_{\frac{1}{7}}\left(25\right)$
Cannot be compared
They are equal
Question 3:   Find $x$ , if ${\mathrm{log}}_{5}\left(x\right)=3$
$5$
$1$
$25$
$125$
Question 4:   Find $x$ , if ${\mathrm{log}}_{x}\left(64\right)=6$
$x=10$
$x=2$
$x=8$
$x=6$
Question 5:   Find $x$ , if ${\mathrm{log}}_{7}\left(5-x\right)={\mathrm{log}}_{49}\left(4\right)$
$x=3$
$x=1$
$x=0$
$x=2$
Question 6:   Find $x$ , if ${\mathrm{log}}_{3}\left(11+2x\right)=2$
$x=-1$
$x=-2$
$x=1$
$x=3\text{}$
Question 7:   Find the value of ${\mathrm{log}}_{7}35-{\mathrm{log}}_{7}5=...$
$4$
$1$
$7$
$5$
Question 8:   Find $x$, if ${\mathrm{log}}_{4}\left(3\right)+{\mathrm{log}}_{4}\left(x\right)={\mathrm{log}}_{4}\left(9\right)$
$x=4$
$x=3$
$x=9$
$x=1$
Question 9:   Find $x$ , if ${\mathrm{log}}_{2}\left(3x-8\right)={\mathrm{log}}_{2}\left(x\right)$
$x=4$
$x=6$
$x=1$
$x=2$
Question 10:   Find $x$ , if ${\left(\frac{1}{7}\right)}^{x}=9$
$x={\mathrm{log}}_{\frac{1}{7}}\left(9\right)$
$x=\frac{1}{7}$
$x=1$
$x=9$