Properties of Logarithms & Log Equations

Front

Write as a single logarithm: log12 + 2logx

Back

log(12x^2)

Front

What is the base of the common logarithm?

Back

10

Front

Solve for x: log2(32) = 3x

Back

x = 5/3

Front

Solve for x: log(x) + log(5) = 1

Back

x = 5/10 = 0.5

Front

What is log5(25)?

Back

2

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

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x

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 p.