Solving Exponential Equations

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In summary, exponential equations involve variables in exponents and are used to model situations of growth or decay at a constant percentage rate. The general process for solving these equations involves isolating the variable and using logarithms, and there are two main types: exponential growth and decay. Common mistakes when solving these equations include forgetting to use logarithms, applying logarithm rules incorrectly, and making sign errors. To check a solution, you can plug it back into the original equation or graph the equation.
  • #1
IndigoSwing4
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There is one problem that I can't seem to figure out how to do, and I was wondering if someone could help me. Problem: 5(2)^3x - 4 = 13 . Most exponential equations I can solve, but its the power of 3x that's messing me up.
 
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As always, the first question is "What have you tried so far ?", so that we can see exactly where you need help. :)
 
  • #3
And another question:How do u usually solve exponential equations and why do you think that the method wouldn't apply here...?

Daniel.
 

What are exponential equations?

Exponential equations involve variables in exponents, such as y = 2^x. They are used to model situations where a quantity is growing or decaying at a constant percentage rate.

What is the general process for solving exponential equations?

The general process for solving exponential equations is to isolate the variable in the exponent and use logarithms to bring it down to the base. Then, solve for the variable using basic algebra techniques.

What are the different types of exponential equations?

There are two main types of exponential equations: exponential growth equations, where the base is greater than 1, and exponential decay equations, where the base is between 0 and 1.

What are some common mistakes when solving exponential equations?

Some common mistakes when solving exponential equations include forgetting to use logarithms to bring the variable down from the exponent, incorrectly applying logarithm rules, and making a sign error when dividing by the coefficient of the variable.

How can I check my solution for an exponential equation?

You can check your solution for an exponential equation by plugging it back into the original equation and making sure it satisfies the equation. You can also check by graphing the equation and seeing if the solution is on the curve.

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