Tests in logarithms

Question 1:
1 pts
Logarithmic functions is the inverses of exponential functions.
Question 2:
1 pts
$\log_{b}(x)=y\Leftrightarrow b^{y}=x$
Question 3:
1 pts
If $f(x)=a^{x}$ and $g(x)=\log_{a}x$ then $f$ and $g$ have the same domain.
Question 4:
2 pts
$$\log 17= \log_{10}17$$
Question 5:
2 pts
Find the inverse of the exponential function $2^{x}=8.$

$x=\log_{2}8$

$x=\log_{8}2$

$2=\log_{x}8$

$8=\log_{2}x$
Question 6:
2 pts
Find the inverse of the exponential function $y=3^x.$

$x = log_y3$

$x = 3logy$

$x = log_3y$

$x = y log3$
Question 7:
2 pts
Find the domain of the function given by $y=\log\left(\dfrac{4-x}{2}\right)-3$

$(4,+\infty)$

$(-\infty,4)$

$(-4,4)$

$(-4,+\infty)$
Question 8:
3 pts
Find the correct logarithmic equation. $$\pi^{4}=x $$

$\log_{4}x=\pi$

$\log_{\pi}4=x$

$\log_{x}\pi=4$

$\log_{\pi}x=4$
Question 9:
3 pts
Find the correct exponential equation. $$\log_{7}x=5 $$

$x = 5^{7}$

$x = 7^{5}$

$7^{x}=5$

$7x^{5}=7$
Question 10:
3 pts
Solve. $$\log_{2}x=9 $$

$2$

$9$

$x=81$

$x=512$

Logarithm definition

$\log_{4}x=\pi$	$\log_{\pi}4=x$
$\log_{x}\pi=4$	$\log_{\pi}x=4$

$x=\log_{2}8$	$x=\log_{8}2$
$2=\log_{x}8$	$8=\log_{2}x$

$x = log_y3$	$x = 3logy$
$x = log_3y$	$x = y log3$

$x = 5^{7}$	$x = 7^{5}$
$7^{x}=5$	$7x^{5}=7$