how would you solve the equation 9^x - 6^x = 4^x ? [Exponential equation]

After watching this video, you would be able to solve the exponential equation 9^x - 6^x = 4^x for the unknown x. Exponential or Indicial Equation An exponential equation is an equation in which the variable appears in the exponent. Examples 1. 2^x = 8 2. 3^(x-1) = 27 3. e^x = 10 Solving Exponential Equations 1. *Same base*: If the bases are the same, equate the exponents. 2. *Different bases*: Use logarithms to solve. Example Solve 2^x = 8 1. *Rewrite 8 as 2^3*: 2^x = 2^3 2. *Equate exponents*: x = 3 Tips 1. *Use logarithms*: For equations with different bases or complex exponents. 2. *Check solutions*: Verify the solution(s) by plugging them back into the original equation. Solving Exponential Equations To solve exponential equations, follow these steps: Same Base 1. Equate the exponents. 2. Solve for the variable. Example 2^x = 2^3 x = ? Different Bases 1. Use logarithms (log or ln). 2. Apply the logarithm to both sides. 3. Use logarithm properties to simplify. Example 2^x = 3 log(2^x) = log(3) x log(2) = log(3) x = log(3)/log(2) Tips 1. *Check the base*: If the bases are the same, equate the exponents. 2. *Use logarithms*: For equations with different bases. 3. *Simplify*: Use logarithm properties to simplify the solution. #exponential #equations #equation #logarithm #logarithmic #logarithmicequations #variables #finding #solving #maths #mathematics #mathematician #mathematicseducation #mathematical #mathstricks #mathsproblems #mathskills #usa #uk #canada #india #indian #olympiad #olympiadmathematics #france #russia #indices #exponential #exponents #quadraticequations #quadratics #factorization #solvingquadraticequations #solvinglinearequations #linearequations #algebra #algebratricks #algebraformula