Final Spiral (Day 3)

Front

Write in logarithmic form: 5^2 = 25

Back

log_5(25) = 2

Front

Condense the logarithms: 2log_5z + 2log_5x + 10log_5y

Back

log_5(x^2z^2y^{10})

Front

Write in exponential form: log_2(1/8) = -3

Back

2^{-3} = 1/8

Front

Expand the logarithm: log_8(x·y·z^6)

Back

log_8(x) + log_8(y) + 6log_8(z)

Front

Evaluate the logarithm using change of base: log_5(83)

Back

2.746

Front

Definition of a logarithm

Back

A logarithm is the exponent to which a base must 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(mn) = 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 real number p.