How to Solve for x in the Power Equation: 2.34=15.3*0.886^x

Thread starter CD01
Start date Aug 27, 2014
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Power

In summary, the power equation is a mathematical formula that represents the relationship between a base number and its exponent. To solve for x in the power equation, you need to isolate the variable by taking the logarithm of both sides of the equation. The purpose of the exponent is to express very large or very small numbers in a more concise form. To check your work when solving for x, you can plug the value back into the original equation or use a calculator to verify your solution.

Aug 27, 2014

CD01

hey, so I just need to know the steps on how to slove for x in this equation
> 2.34=15.3*0.886^x
thanks.

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Aug 27, 2014

NascentOxygen

Staff Emeritus

Science Advisor

Hi CD01. Welcome to the famous Physics Forums.

Do you know about logarithms?

Aug 27, 2014

HallsofIvy

Science Advisor

Homework Helper

Ah more "sloving"! It should be an obvious first step to divide both sides by 15.3 to get
[tex]0.886^x= \frac{2.34}{15.3}[/tex]

Now, as NascentOxygen said, use a logarithm.

1. What is the power equation and how does it work?

The power equation is a mathematical formula that represents the relationship between a base number and its exponent. It is written as a^b, where a is the base number and b is the exponent. The equation is solved by raising the base number to the power of the exponent. For example, 2^3 would be solved as 2*2*2, which equals 8.

2. How do I solve for x in the power equation?

To solve for x in the power equation, you need to isolate the variable on one side of the equation. In this case, you would need to isolate the exponent, which is represented by x. You can do this by taking the logarithm of both sides of the equation. The specific logarithm you use will depend on the base number in the equation.

3. How do I use logarithms to solve for x?

To use logarithms to solve for x, you first need to identify the base number of the logarithm. In this equation, the base number is 0.886. Then, take the logarithm of both sides of the equation using that base number. This will give you an equation in the form of log(base number)(2.34) = x. You can then use a calculator to solve for x.

4. What is the purpose of the exponent in the power equation?

The exponent in the power equation represents the number of times the base number is multiplied by itself. It is used to express very large or very small numbers in a more concise form. For example, instead of writing out 2*2*2*2*2, we can use the power equation 2^5 to represent the same value.

5. How can I check my work when solving for x in the power equation?

You can check your work by plugging the value you solved for x back into the original equation. If the equation holds true, then your answer is correct. You can also use a calculator to verify that your solution is correct by plugging in the original equation and the value of x you solved for. If the calculator gives you a value close to the original equation, then your solution is likely correct.