Solving Exponentials Using Logarithms

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number. For example, if b^y = x, then log_b(x) = y.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

To convert an exponential equation a^b = c to logarithmic form, you write it as log_a(c) = b.

Tags

CCSS.HSF.BF.B.5

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in log_2(8) = 3, the base is 2.

Tags

CCSS.HSF.BF.B.5

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_a(b) = log_c(b) / log_c(a) for any positive c.

Front

How do you solve an exponential equation using logarithms?

Back

To solve an exponential equation, take the logarithm of both sides, then use properties of logarithms to isolate the variable.

Front

What is the property of logarithms that states log_a(m * n) = ?

Back

log_a(m) + log_a(n) (the product property of logarithms).

Front

What is the property of logarithms that states log_a(m/n) = ?

Back

log_a(m) - log_a(n) (the quotient property of logarithms).

Front

What is the property of logarithms that states log_a(m^n) = ?

Back

n * log_a(m) (the power property of logarithms).

Front

Solve for x: 4^(x+2) = 64

Back

x = 1.

Tags

CCSS.HSF.LE.A.4