Exp/Log Test Review

Front

What is the value of log₄1?

Back

0

Front

Solve the equation: 4^{2x} = 7

Back

x = 0.702

Front

Solve: log₆(2x + 3) = 3

Back

x = 106.5

Front

Solve: ln(3x + 2) = ln(5x - 6)

Back

x = 4

Front

Solve for a: 5^{a + 2} = 1/125

Back

a = -5

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 natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.

Front

What is the relationship between exponents and logarithms?

Back

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

Front

What is the product rule for logarithms?

Back

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