Calculus Bowl 3 (logs + exponentials)

Front

Evaluate log₄1

Back

0

Front

Solve for x: 5 e^x = 1.5

Back

-1.2

Front

What is the derivative of ln(x³)?

Back

Front

Rewrite log_pt = m in exponential form.

Back

p^m = t

Front

Evaluate 2^-5

Back

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number.

Front

What is the change of base formula for logarithms?

Back

Front

What is the natural logarithm?

Back

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

Front

What is the relationship between exponents and logarithms?

Back

If b^x = a, then log_ba = x.

Front

What is the product rule for logarithms?

Back

log_b(xy) = log_bx + log_by.