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

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