Properties of Logarithms

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

What is the property of logarithms that allows you to rewrite log_b(x^n)?

Back

log_b(x^n) = n * log_b(x)

Front

How do you combine logarithms using subtraction and addition?

Back

log_a(b) - log_a(c) = log_a(b/c) and log_a(b) + log_a(c) = log_a(b*c)

Front

Rewrite the expression log(6) - log(3) + 2*log(7) as a single logarithm.

Back

log(98)

Front

What is the logarithmic form of the equation 3^4 = 81?

Back

log_3(81) = 4

Front

Evaluate log_b(b).

Back

1

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 value of log_10(10^3)?

Back

3

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