Exponential and Log Equations + Condensing and Expanding

Front

Evaluate e^ln6

Back

6

Front

Solve for x: e^(x+6) + 5 = 1

Back

No Solution

Front

Write as a single log: log 12 + 2 log x

Back

log (12x^2)

Front

Solve for x: 3^(x-2) = 5^(2x-3)

Back

(2log3-3log5)/(log3-2log5)

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

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) - 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.

Front

Definition: Natural Logarithm

Back

The logarithm to the base e, denoted as ln(x), where e is approximately 2.718.