Log/Exponential Function Recap PC

Front

Convert 16 = 2^x to a Log

Back

Log_2(16) = x

Front

Solve: log_3(x - 5) = 2

Back

x = 14

Front

Katy deposited $90 in a savings account earning 5% interest, compounded quarterly. Which equation represents the amount of money in her account yearly?

Back

A = 90(1 + 0.05/4)^(4t) where A is the amount after t years.

Front

Convert Log_2(64) = y to an exponent

Back

2^y = 64

Front

If you invest $5,000 into an account paying 6% interest compounded continuously, how many years until there is $8,000?

Back

t = 7.83 years

Front

Definition of a logarithm

Back

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

Front

Change of Base Formula for Logarithms

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Properties of Logarithms: Product Rule

Back

log_b(m * n) = log_b(m) + log_b(n) for any positive m and n.

Front

Properties of Logarithms: Quotient Rule

Back

log_b(m / n) = log_b(m) - log_b(n) for any positive m and n.

Front

Properties of Logarithms: Power Rule

Back

log_b(m^p) = p * log_b(m) for any positive m and p.