7.9 Log & Exponential Equations

Front

Change to Exponential Form: log₆36 = 2

Back

6² = 36

Front

Solve for x: 2^(3x + 1) = 32

Back

x = 4/3

Front

Change to Logarithmic Form: 5³ = 125

Back

log₅ 125 = 3

Front

Solve: 9^(8-x) = 27^(x-3)

Back

x = 5

Front

Solve: log(x + 6) = 1

Back

x = 4

Front

Definition: Logarithm

Back

The logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised, to produce a given number?

Front

Definition: Exponential Function

Back

A 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

Property: log_b(mn)

Back

log_b(m) + log_b(n) - The logarithm of a product is the sum of the logarithms.

Front

Property: log_b(m/n)

Back

log_b(m) - log_b(n) - The logarithm of a quotient is the difference of the logarithms.

Front

Property: log_b(m^k)

Back

k * log_b(m) - The logarithm of a power is the exponent times the logarithm of the base.