Logarithms

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3 81 = 4

Front

Solve for x: 5^x = 17.

Back

x = log_5 17

Front

What is the exponential form of log_2 32 = 5?

Back

2^5 = 32

Front

Expand: log_8 (xyz^5).

Back

log_8 x + log_8 y + 5 log_8 z

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

If log_b a = c, what is the equivalent exponential form?

Back

b^c = a

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 rule for logarithms?

Back

log_b (xy) = log_b x + log_b y.

Front

What is the quotient rule for logarithms?

Back

log_b (x/y) = log_b x - log_b y.

Front

What is the power rule for logarithms?

Back

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