11MA End of S1 Review

Front

Back

The domain is (1, ∞).

Front

What is the value of log₅25?

Back

The value is 2.

Front

Solve for x: 5^{-3x - 1} = 25.

Back

x = -1.

Front

Write the expression as a single logarithm: log₅3 + log₅6 + log₅9.

Back

The expression simplifies to log₅162.

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 base of a logarithm?

Back

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

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_c(a) / log_c(b) for any base c.