0. Functions

Logarithmic Functions

0. Functions

Logarithmic Functions

Struggling with Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Convert the following logarithmic expression to its equivalent exponential form.
$\log_4x=5$

$4^{x}=5$

$x^4=5$

$4^5=x$

$5^4=x$

Verified step by step guidance

Identify the given logarithmic expression:

\log 4_{x} = 5

Recall the definition of a logarithm:

\log b_{a} = c

means

b_{c} = a

Apply the definition to the given expression:

4_{5} = x

Verify the conversion by checking if the exponential form correctly represents the original logarithmic statement.

Conclude that the exponential form of the given logarithmic expression is

4_{5} = x

7:3m

Watch next

Master Logarithms Introduction with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.

c. ln (x + y) = ln x + ln y

views

Textbook Question

Logarithm properties Use the integral definition of the natural logarithm to prove that ln(x/y) = ln x - ln y.

views

Textbook Question

Falling body When an object falling from rest encounters air resistance proportional to the square of its velocity, the distance it falls (in meters) after t seconds is given by d(t) = (m/k) ln (cosh (√(kg/m) t)), where m is the mass of the object in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant.

a. A BASE jumper (m = 75 kg) leaps from a tall cliff and performs a ten-second delay (she free-falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume k = 0.2.

views

Textbook Question

ln x is unbounded Use the following argument to show that lim (x → ∞) ln x = ∞ and lim (x → 0⁺) ln x = −∞.

c. Show that ln 2ⁿ > n/2 and ln 2^(−n) < −n/2.

views

Multiple Choice

Convert the following logarithmic expression to its equivalent exponential form.

$x=\log9$

Convert the following exponential expression to its equivalent logarithmic form.

$3^{x}=7$

Convert the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

{Use of Tech} Let f(x) = ln((x+1)/(x-1)) and g(x) = ln ((x+1)/(x-1)).

b. Sketch graphs of f and g to show that these functions do not differ by a constant.

110

views

Show more practices

Logarithmic Functions practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice

Struggling with Calculus?

Convert the following logarithmic expression to its equivalent exponential form.log4x=5\log_4x=5log4x=5

Watch next

Logarithmic Functions practice set

Convert the following logarithmic expression to its equivalent exponential form.
$\log_4x=5$