Logarithmic properties

Question 1:
1 pts
$$a^{\log_{a}x}=x$$
Question 2:
1 pts
$$\log_{a}b=\dfrac{\log_{c}b}{\log_{c}a}$$
Question 3:
1 pts
Simplify. $$\log_{a^{s}}x$$

$s\log_{a}x$

$\dfrac{1}{s}\log_{a}x$

$\log_{a}x^{s}$

none of these
Question 4:
1 pts
Find the correct property for $\log_{a}b.$

$-\dfrac{1}{\log_{b}a}$

$\dfrac{1}{\log_{b}a}$

$-\log_{b}a$

$\dfrac{1}{\log ab}$
Question 5:
2 pts
Simplify. $$\log_{10}(\log_{4}(\log_{3}81))$$

$3$

$4$

$1$

$0$
Question 6:
2 pts
Evaluate. $$\dfrac{\log_{2}36}{\log_{2}6}$$

$1$

$2$

$4$

$6$
Question 7:
2 pts
Evaluate. $$\log_{3}5\cdot \log_{4}9\cdot \log_{5}2$$
Question 8:
2 pts
Find $x$ from equation $\log_{3}x=3\log_{3}a+2\log_{3}c.$

$x=a^{3}c^{3}$

$x=a^{2}c^{2}$

$x=ac^{3}$

$x=a^{3}c^{2}$
Question 9:
3 pts
If $\log 5=a$ and $\log 3=b$ evaluate $\log_{30}8$.

$\log_{30}8=$
Question 10:
3 pts
Simplify. $$\log_{3}2\cdot\log_{4}3\cdot\log_{5}4\cdot\log_{6}5\cdot\log_{7}6\cdot\log_{8}7$$

$\dfrac{2}{3}$

$\dfrac{1}{3}$

$\dfrac{1}{4}$

$\dfrac{2}{5}$
Question 11:
3 pts
If $\log_{14}7=a$ and $\log_{14}5=b$ then

$\log_{35}20 = $
Question 12:
3 pts
$$\log_{3}7=\log_{\frac{1}{3}}{\dfrac{1}{7}}$$

Exponents

$s\log_{a}x$	$\dfrac{1}{s}\log_{a}x$
$\log_{a}x^{s}$	none of these

$3$	$4$
$1$	$0$

$x=a^{3}c^{3}$	$x=a^{2}c^{2}$
$x=ac^{3}$	$x=a^{3}c^{2}$

$\dfrac{2}{3}$	$\dfrac{1}{3}$
$\dfrac{1}{4}$	$\dfrac{2}{5}$