Solving 3^x=200, x^3=200, cube root of x = 5, and log base 3 of x = 5

TL;DR

This video discusses how to solve equations with exponents and logarithms using specific techniques.

Transcript

okay we are going to solve for these four equations and notice that they all look kind of similar to each other right but make sure that you know the correct steps to stop each and every one for the first one we have 3 to the X is equal to 200 and you see that the ex is in the exponent so in this case we have to do logarithm on both sides and let m... Read More

Key Insights

• ❓ Equations with exponents and logarithms require specific techniques to solve.
• ⚾ For equations with exponents, determining whether the variable is in the base or the exponent is crucial for selecting the correct method.
• 🥡 Taking logarithms helps to isolate the variable when it is in the exponent.
• 🫚 Using roots can cancel out the exponent when the variable is in the base.
• ⚾ Calculators may require using the change of base formula for specific logarithm bases.
• ❓ Logarithmic equations can be solved by rewriting them as exponential equations.
• 🅰️ Understanding properties of exponents and logarithms is essential for solving these types of equations.

Questions & Answers

Q: What is the first step in solving an equation with an exponent?

The first step is to determine whether the variable is in the base or the exponent. If the variable is in the exponent, you should take the logarithm on both sides using the appropriate base to isolate the variable.

Q: How do you solve an equation with a variable in the base?

If the variable is in the base, you should take the appropriate root on both sides to cancel out the exponent. For example, if the exponent is 3, you would take the cube root.

Q: What if the calculator does not have a specific logarithm base?

If the calculator does not have a logarithm function for a specific base, you can use the change of base formula. Divide the logarithm of the number by the logarithm of the base to find the solution.

Q: Can you explain how to solve a logarithmic equation?

To solve a logarithmic equation, you should rewrite it as an exponential equation. In other words, make the exponent the subject and raise the base to that exponent. Then solve for the variable.

Summary & Key Takeaways

• The video explains how to solve four different equations that involve exponents and logarithms.

• For each equation, specific steps are outlined, such as taking logarithms or applying roots, to isolate the variable.

• The video also provides alternative methods, such as using logarithm properties or calculator tricks, to find the solutions.