Flashcardzizz 5 Alg2H

Front

What is the natural logarithm of a number?

Back

The natural logarithm, denoted as \ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828. It answers the question: to what power must e be raised to obtain the number x.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If \(y = e^x\), then \(x = \ln(y)\).

Front

How do you convert an exponential equation to a logarithmic form?

Back

To convert an exponential equation \(a^b = c\) to logarithmic form, use the formula \(b = \log_a(c)\).

Front

What is the value of \(\ln(e)\)?

Back

The value of \(\ln(e)\) is 1, because e raised to the power of 1 equals e.

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, which is approximately 2.718.

Front

What does the expression \(e^x = 24\) imply?

Back

It implies that \(x = \ln(24)\), meaning x is the power to which e must be raised to equal 24.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is \(A = P(1 + r)^t\), where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What does a growth rate of 2% mean in an exponential function?

Back

A growth rate of 2% means that the quantity increases by 2% of its current value each time period.

Front

How do you solve for x in the equation \(e^x = 5\)?

Back

To solve for x, take the natural logarithm of both sides: \(x = \ln(5)\).

Front

What is the equivalent logarithmic form of \(7^x = 24\)?

Back

The equivalent logarithmic form is \(x = \log_7(24)\).