Logarithms and Exponentials Test

Front

Rewrite log_p(t) = m in exponential form.

Back

p^m = t

Front

Convert 6^(x+2) = 216 to logarithmic form.

Back

log_6(216) = x + 2

Front

Use multiple log properties to write as a sum or difference of two logs: log(4x^3).

Back

log 4 + 3log x

Front

Write in logarithmic form: 2^(-4) = 1/16.

Back

log_2(1/16) = -4

Front

Convert log(x) = 5 to exponential form.

Back

10^5 = x

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

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