Examples of Exponential Equations
2x=482x=1616x+1=256(12)x+1=512
As you might've noticed, an exponential equation is just a special type of equation. It's an equation that has exponents that are variables.
2x=482x=1616x+1=256(12)x+1=512
As you might've noticed, an exponential equation is just a special type of equation. It's an equation that has exponents that are variables.
There are different kinds of exponential equations. We will focus on exponential equations that have a single term on both sides. These equations can be classified into 2 types.
4x=49.
Solve: 4x+1=49
Step 1Ignore the bases, and simply set the exponents equal to each other
x+1=9
Step 2Solve for the variable
x=9−1x= 8
CheckWe can verify that our answer is correct by substituting our value back into the original equation . .
4x+1=4948+1=49
49=49
Enter any exponential equation into the algebra solver below :
43=2x
9x=81
(12)x+1=43
42x+1=65
In each of these equations, the base is different. Our goal will be to rewrite both sides of the equation so that the base is the same.
Solve: 43=2x
Step 1Forget about the exponents for a minute and focus on the bases:
Rewrite the bases as powers of a common base. Do this by asking yourself :
Answer: They are both powers of 2
Rewrite equation so that both exponential expressions use the same base
43=2x(22)3=2x
Use exponents laws to simplify
(22)3=2x(22⋅3)=2x(26)=2x
Solve like an exponential equation of like bases
(26)=2xx=6
Substitute 6 into the original equation to verify our work.
43=26
64=64
Unlike bases often involve negative or fractional bases like the example below. We are going to treat these problems like any other exponential equation with different bases--by converting the bases to be the same.