We need to understand the exponential equation before how to solve the exponential equation. Exponential equation is a function which can be understood through the given equation.
F(x) = abx
In the above formula b is a positive real number and x is exponent. Equations where variables occur as exponents are known as Exponential equations.
Exponential equation can be solved by
- Exponential equation solving with same base
- Exponential equation solving with different bases.
- Solving Exponential equation and whole number.
- Solving the exponential equation using logarithms.
How to solve the exponential equation with the same bases?
The following steps can be applied to solve the exponential equation with same bases;
It means if the bases are the same then the exponents must be the same. How to solve the exponential equation can be obtained by using steps given below.
Step 1: Whether the number can be written using the same base should be determined. If the number can be written using the same base so stop and use others steps for solving Exponential equations with the same base. If not, step 2 is required.
Step 2: Problem using the same base should be rewritten.
Step 3: Simplifying the problem using the properties of exponents.
Step 4: drop the bases and set the exponents equal to each other when the bases are the same.
Step 5: By isolating the variable, finish the problems.
Step 6: whether the answer is correct or not we can see by plugging the solution found by into the original equations. Both sides of the equation should be equal after simplifying each expression.
Let us understand how to solve the exponential equation through example.
Solve :42x−1=64
Applying the above step:
Here there are no same bases. Accordingly, we need to convert 64 in such a form so that the base can be the same. It can be done by rewriting 64 as 43.
Putting the value 43 in respect of 64, The equation is as:
42x−1= 43
Rule of the equation denoted that where the bases are the same, the exponent should be equal. Applying the property of equality of exponential function, the equation can be rewrite as follows:
2x-1 = 3
Hence, The equation indicates that x is equal to 1.
How to solve the exponential equations with different Bases?
Steps for solving Exponential equations with different bases is as follows:
Sometimes we are given exponential equations with different bases on the terms. In order to solve these equations, we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.
Step1: Whether the number can be written using the same base should be determined. If the number can be written using the same base so stop and use others steps for solving Exponential equations with the same base. If not, step 2 is required.
Step2: Common logarithm or natural logarithm of each side should be taken.
Step3: Rewriting the problem by using the properties of logarithm.
Step4: Using the logarithm to divide each side.
Step5: With the help of a calculator , find the decimal approximation of the logarithm.
Step6: By isolating the variable, finish the problems.
Step7: Logs in the equation should be found by using a scientific calculator. Type the number finding the log of, then hit the LOG button.
Step 8: competing the calculations as this will give the value of variables. Answer will be in approximate since it has been rounded off when finding the logs.
How to solve the exponential equations with whole numbers?
The following steps can be applied for solving the exponential equations with whole numbers.
Step 1: Exponential equations should be isolated. There must be Exponential expression on one side of the equation and whole numbers on another side. If Exponential expression and the whole number is not on one side, rework the equation so that the exponent is alone on one side.
Step 2: whether the whole number can be converted to an exponent with the same base as the other exponent should be determined. If it cannot convert into a whole number this method cannot be used.
Step 3: After converting into the whole number, there are two Exponential expressions with the same base. Ignore and focus on the exponent since the bases are the same.
Step 4: By isolating the variable, finish the problems.
Step 5: whether the answer is correct or not we can see by plugging the solution found by into the original equations. Both sides of the equation should be equal after simplifying each expression.
How to solve the exponential equations using logarithms?
The following steps can be followed to solve the exponential equations using logarithms:
Step 1: Any exponential expression should be kept at one side of the equation.
Step 2: It needs to get a log on both sides of the equation. Any bases can be used for log.
Step 3: Variable should be solved using the basic logarithm rules.
Conclusion
The answers to the question of how to solve the exponential equation can be done by applying two methods. The first method requires use of a special form of exponential function and it can be solved easily. However, the second one is a little bit complicated to solve. The exponential equation can be solved by using several rules such as property rule, logarithm, replacement and other different formulas. Get the best math homework solver from us and score good grades in your math homework.
