Solve each equation. x = log￬8 ∜8

Key Concepts

Logarithms

Logarithms are the inverse operations of exponentiation. They answer the question: to what exponent must a base be raised to produce a given number? For example, in the expression log_b(a) = c, b^c = a. Understanding logarithms is essential for solving equations involving them, as they allow us to manipulate exponential relationships.

Change of Base Formula

The Change of Base Formula allows us to convert logarithms from one base to another, which is particularly useful when using calculators that typically only compute logarithms in base 10 or base e. The formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number. This concept is crucial for solving logarithmic equations when the base is not easily computable.

Exponential Equations

Exponential equations involve variables in the exponent and can often be solved using logarithms. For instance, if we have an equation like a^x = b, we can take the logarithm of both sides to isolate x. Understanding how to manipulate and solve exponential equations is key to finding solutions in problems involving logarithms.