Exponentials and Logarithms Review

Front

Rewrite log_b(x^n)

Back

nlog_b(x)

Front

The common logarithm has what base?

Back

10

Front

What does i^2 = ?

Back

-1

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4

Front

Simplify 3i - (4 + 7i)

Back

-4 - 4i

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 relationship between exponents and logarithms?

Back

If b^y = x, then log_b(x) = y.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_b(x) + log_b(y).