How To Solve Equation With Exponent Variable

Its an equation that has exponents. 2 and -2 since 2 2 4 and -2 2 4.

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F x ab x In the above formula b is a positive real number and x is exponent.

How to solve equation with exponent variable. Both of the variables are squared in this equation and are being raised to the power of three. ρ b ρ f ϕ m where ρ b is the bulk resistivity ρ f is the fluid resistivity ϕ is the porosity and m 0 is a cementation exponent. You will need to divide each side of the equation by the log of the exponential.

First rewrite each side of the equation using the same base. Because if two exponential terms are equal with same base then their exponents also must be equal. This gives you A BC.

There are two methods for solving exponential equations. After rewriting exponential equations with same base on both sides we can compare the powers. Equate the exponents and solve for the unknown variable.

Equate the exponents of the same bases. Equations where variables occur as exponents are known as Exponential equations. The other will work on more complicated exponential equations but can be a little messy at times.

Now we need to get rid of the C which is currently on the same side of the equation as B. If the exponent is an odd power there is only one solution. 8 8 64 When we solve an equation we figure out what value of x or any other variable makes the statement true satisfies the equation.

For example if youre asked to solve 4 x 2 64 you follow these steps. Whenever an equation contains all even exponents you should consider both the positive and negative solutions. Usually we use something called Archies Law.

Equation 1 has two solutions. In my case the porosity ϕ is unknown.

Identify the exponential. Solving Equations with Exponents. Lets start off by looking at the simpler method.

Solve to find the value of variable. The basic type of exponential equation has a variable on only one side and can be written with the same base for each side. To solve you need to rewrite the equation so that one side contains the variable and the other side contains all of the numbers.

Isolate the variable. One method is fairly simple but requires a very special form of the exponential equation. Rewrite both sides of the equation so that the bases match.

Consider these two equations. By taking the log of an exponential we can then move the variable being in the exponent thats now inside a log out in front as a multiplier on the log. Invert the operations that were applied to the exponential in the reverse order in which they were applied.

Using the property of the exponents multiply the powers of each base. The basic type of exponential equation has a variable on only one side and can be written with the same base for each side. In this case you can do that by multiplying both sides of the equation by B.

Rewrite both sides of the equation so that the bases match. By using the multiplication table we know that the number is 8. Exponential equation is a function which can be understood through the given equation.

A good way to start would be to get the B on top of a fraction rather than on the bottom. However if the number set you gave were to equal something then it would be possible to find A but without that you cannot solve a problem if they do not give you what the letter is. For example if youre asked to solve 4 x 2 64 you follow these steps.

The best you can do is to simplify the equation which would mean that you use PEMDAS on all of the numbers and the variable would have to stay. Equation 2 only has one solution.

In this equation the power of three needs to be distributed to both the 𝒙 and the 𝑦 variables. The result is that the exponential stands alone on one side of the equation which now has the form b f a. Examples of Exponential Equations 2 x 4 8 2 x 16 16 x 1 256 1 2 x 1 512 As you mightve noticed an exponential equation is just a special type of equation.

In other words the log rule will let us move the variable back down onto the ground where we can get our hands on it.

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