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 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.

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.

Front

What is the base of a logarithm?

Back

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

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

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

Back

x = 1.

Front

Solve for x: 4^(6x-12) = 7

Back

x = 2.23.

Front

Solve for x: 5^(x-6) = 18

Back

x = 7.8.

Front

Solve for x: 7^x = 36

Back

x = 1.8416.

Front

Solve for x: 5(6^(3x)) = 20

Back

x = 0.26.