# Test: Logarithms II - Challenging

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Question 1:   Find $x$: $2={\mathrm{log}}_{8}x$
$49$
$256$
$16$
$64$
Question 2:   Find $x$: $x={\mathrm{log}}_{3}243$
$9$
$27$
$5$
$81$
Question 3:   Solve ${\mathrm{log}}_{2}8+{\mathrm{log}}_{8}2$
$3\frac{1}{3}$
$4$
$1$
$16$
Question 4:   Express ${\mathrm{log}}_{7}x$ as multiple of ${\mathrm{log}}_{10}x$
${\mathrm{log}}_{10}x-{\mathrm{log}}_{3}x$
${\mathrm{log}}_{10}x{\mathrm{log}}_{3}x$
${\mathrm{log}}_{10}x{\mathrm{log}}_{7}10$
$\frac{{\mathrm{log}}_{10}x}{{\mathrm{log}}_{3}x}$
Question 5:   Express ${\mathrm{log}}_{4}17$ in terms of the logarithms base $10$
${\mathrm{log}}_{10}17/{\mathrm{log}}_{10}4$
${\mathrm{log}}_{10}4/{\mathrm{log}}_{10}17$
$17{\mathrm{log}}_{10}4$
$4{\mathrm{log}}_{10}17$
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