Logarithm definition

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 $y=\log\left(\dfrac{4-x}{2}\right)-3$

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. $$\log_{2}x=9 $$

Exponents