finding the base of a logarithmic equation

After watching this video, you would be able to find the base of a logarithmic equation. Logarithms Definition A logarithm is the inverse operation of exponentiation. It asks, "To what power must the base be raised to get the given value?" Notation logₐ(x) = y ⇔ a^y = x Types 1. *Common logarithm*: log₁₀(x) 2. *Natural logarithm*: ln(x) = logₑ(x) Properties 1. *Product rule*: logₐ(MN) = logₐ(M) + logₐ(N) 2. *Quotient rule*: logₐ(M/N) = logₐ(M) - logₐ(N) 3. *Power rule*: logₐ(M^p) = p logₐ(M) Applications 1. *Mathematics*: solving equations, calculus 2. *Science*: physics, chemistry, biology 3. *Computer science*: algorithms, data analysis Key Concepts 1. *Base*: the number being raised to a power 2. *Argument*: the value inside the logarithm Practice Try applying the properties of logarithms to simplify expressions! Solving Logarithmic Equations Steps 1. *Isolate the logarithm*: get the logarithm alone on one side of the equation. 2. *Exponentiate both sides*: use the base of the logarithm to eliminate the logarithm. 3. *Solve for the variable*: simplify and solve for the variable. Example Solve for x: log₂(x) = 3 1. *Exponentiate both sides*: 2^log₂(x) = 2^3 2. *Simplify*: x = 8 Tips 1. *Check the domain*: ensure the argument of the logarithm is positive. 2. *Use properties of logarithms*: apply properties like log(a) + log(b) = log(ab) to simplify equations. Practice Try solving: log₃(x) = 2 #logarithm #solving #finding #base #logarithmicequation #solvingequations #maths #mathematics #usa #canada #uk #china #russia #brasil