Exponential Equation Calculator is a free online tool that solves the given exponential equation and gives the variable value. BYJU’S online exponential equation calculator tool makes the calculations faster and solves the exponential equation in a fraction of seconds.
How to Use the Exponential Equation Calculator?
The procedure to use the exponential equation calculator is as follows:
Step 1: Enter the exponential equation a given input field
Step 2: Click the button “Submit” to get the result of the exponential equation
Step 3: Finally, the value of the variable will be displayed in the new window
What is an Exponential Equation?
In Algebra, an exponential equation is an equation in which a variable occurs in the exponents. In case both the sides of an equation have the same bases, then by the property, ax = ay, then the exponent values should be equal to each other. It means that, x = y.
Consider an exponential equation, 5x+1 = 59
Since the bases on both sides are equal, then
x+1 = 9
x = 8
Standard Form
The standard form to represent the exponential function is as follows. An exponential function with base “b” is given by:
f (x) = abx
Where x is a real number, a ≠ 0, b>0, and b ≠1
Here, the exponent “x” is a variable, and the base “b” is a constant.
Frequently Asked Questions on Exponential Equation Calculator
The laws of exponents are:What are the laws of exponents?
What are the applications of the exponential function?
The most important applications of the exponential functions are:
- Exponential decay
- Compound interest
- Population growth
What is an exponential constant?
An exponential constant is one of the most important mathematical constants and it is denoted by the letter “e”. The value of e is approximately equal to 2.718
Calculator Use
This calculator will solve for the exponent n in the exponential equation xn = y, stated x raised to the nth power equals y. Enter x and y and this calculator will solve for the exponent n using log(). Since taking the log() of negative numbers causes calculation errors they are not allowed.
How to solve for exponents
For xn = y; solve for n by taking the log of both sides of the equation:
For:
\( x^n = y \)
Take the log of both sides:
\( \log_{}x^n = \log_{}y \)
By identity we get:
\( n \cdot \log_{}x = \log_{}y \)
Dividing both sides by log x:
\( n = \dfrac{\log_{}y}{\log_{}x} \)
Find the exponent of a number
For the equation 3n = 81 where 3 is called the base and n is called the exponent, find the value of the exponent n using logarithms.
For:
\( 3^n = 81 \)
Take the log of both sides:
\( \log_{}3^n = \log_{}81 \)
By identity we get:
\( n \cdot \log_{}3 = \log_{}81 \)
Dividing both sides by log 3:
\( n = \dfrac{\log_{}81}{\log_{}3} \)
Using a calculator we can find that log 81 ≈ 1.9085 and log 3 ≈ 0.4771 then our equation becomes:
\( n = \dfrac{\log_{}81}{\log_{}3} \approx \dfrac{1.9085}{0.4771} \approx 4 \)
Checking our answer 34 = 81.
Since taking the log() of negative numbers, 0 or 1 causes calculation errors we have provided some answers by definition and not actual calculations.
Calculator Use
This is an online calculator for exponents. Calculate the power of large base integers and real numbers. You can also calculate numbers to the power of large exponents less than 2000, negative exponents, and real numbers or decimals for exponents.
For larger exponents try the Large Exponents Calculator
For instructional purposes the solution is expanded when the base x and exponent n are small enough to fit on the screen. Generally, this feature is available when base x is a positive or negative single digit integer raised to the power of a positive or negative single digit integer. Also, when base x is a positive or negative two digit integer raised to the power of a positive or negative single digit integer less than 7 and greater than -7.
For example, 3 to the power of 4:
\( x^n = \; 3^{4} \)
\( = \;3 \cdot 3 \cdot 3 \cdot 3 \)
\( = 81 \)
For example, 3 to the power of -4:
\( x^n = \;3^{-4} \)
\( = \dfrac{1}{3^{4}} \)
\( = \; \dfrac{1}{3 \cdot 3 \cdot 3 \cdot 3} \)
\( = \; \dfrac{1}{81} \)
\( = 0.012346 \)
Exponent Notation:
Note that -42 and (-4)2 result in different answers: -42 = -1 * 4 * 4 = -16, while (-4)2 = (-4) * (-4) = 16. If you enter a negative value for x, such as -4, this calculator assumes (-4)n.
"When a minus sign occurs with exponential notation, a certain caution is in order. For example, (-4)2 means that -4 is to be raised to the second power. Hence (-4)2 = (-4) * (-4) = 16. On the other hand, -42 represents the additive inverse of 42. Thus -42 = -16. It may help to think of -x2 as -1 * x2 ..."[1]
Examples:
- 3 raised to the power of 4 is written 34 = 81.
- -4 raised to the power of 2 is written (-4)2 = 16.
- -3 raised to the power of 3 is written (-3)3 = -27. Note that in this case the answer is the same for both -33 and (-3)3 however they are still calculated differently. -33 = -1 * 3 * 3 * 3 = (-3)3 = -3 * -3 * -3 = -27.
- For 0 raised to the 0 power the answer is 1 however this is considered a definition and not an actual calculation.
Exponent Rules:
\( x^m \cdot x^n = x^{m+n} \)
\( \dfrac{x^m}{x^n} = x^{m-n} \)
\( (x^m)^n = x^{m \cdot n} \)
\( (x \cdot y)^m = x^m \cdot y^m \)
\( \left(\dfrac{x}{y}\right)^m = \dfrac{x^m}{y^m} \)
\( x^{-m} = \dfrac{1}{x^m} \)
\( \left(\dfrac{x}{y}\right)^{-m} = \dfrac{y^m}{x^m} \)
\( x^1 = x \)
\( x^0 = 1 \)
\( 0^0 = 1 \; (definition) \)
\( if \; x^m = y \; then \; y = \sqrt[m]{x} = y^{\frac{1}{m}} \)
\( x^{\frac{m}{n}} = \sqrt[n]{x^m} \)
References
[1] Algebra and Trigonometry: A Functions Approach; M. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Company; 1982, page 11.
For more detail on Exponent Theory see Exponent Laws.
To calculate fractional exponents use our Fractional Exponents Calculator.
To calculate root or radicals use our Roots Calculator.
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