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 $\log_{a}b.$

Question 5:

2 pts

Simplify. $$\log_{10}(\log_{4}(\log_{3}81))$$

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

Question 6:

2 pts

Evaluate. $$\dfrac{\log_{2}36}{\log_{2}6}$$

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