SOlving logs 2024 (non combine)

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. For example, if b^y = x, then log_b(x) = y.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

How do you solve the equation log_b(x) = y for x?

Back

To solve log_b(x) = y, rewrite it in exponential form: x = b^y.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(m^p) = p * log_b(m).

Front

How do you isolate a logarithm in an equation?

Back

To isolate a logarithm, you can use algebraic operations to move other terms to the opposite side of the equation.

Front

What is the value of log_9(89) when log_9(r-8) = 2?

Back

The value of r is 89.

Front

How do you solve the equation 2log_3(x+1) = 6?

Back

First, divide both sides by 2 to get log_3(x+1) = 3, then convert to exponential form: x + 1 = 3^3, so x = 26.

Front

What is the solution to the equation -8 + log_6(x + 1) = -7?

Back

To solve, add 8 to both sides to get log_6(x + 1) = 1, then convert to exponential form: x + 1 = 6^1, so x = 5.