Review: Solving Exponentials

Front

Expand: log (x²y³)

Back

2log x + 3 log y

Front

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

Back

x = 2

Front

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

Back

x = 5

Front

Condense: 4log a - 5 log b

Back

log (a⁴/b⁵)

Front

Solve for x: 5^x = 17

Back

x = log₅ 17

Front

Definition: Exponential Function

Back

A function of the form f(x) = a * b^x, where a ≠ 0, b > 0, and b ≠ 1.

Front

Definition: Logarithm

Back

The inverse operation to exponentiation, defined as log_b(a) = c if and only if b^c = a.

Front

Property: log_b(mn)

Back

log_b(m) + log_b(n) (Product Property of Logarithms)

Front

Property: log_b(m/n)

Back

log_b(m) - log_b(n) (Quotient Property of Logarithms)

Front

Property: log_b(m^k)

Back

k * log_b(m) (Power Property of Logarithms)