Solve 2^(x + 1) = 32
Exponential equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 4 |
Step-by-step solution
5 steps-
1 Given2^{x + 1} = 32
Solve for x.
-
2 Isolate the exponential term2^{x} = 16
-
3 Write the right side as a power of 2
Powers with different bases are hard to compare. Facts like 8 = 2³ and 1/4 = 2⁻² rewrite every power with the same base 2; then the exponents can be compared, or the power replaced by a single unknown.
2^{x} = 2^{4} -
4 Same base on both sides, so the exponents must be equal
An exponential function with a positive base other than 1 never takes the same value twice, so bᵐ = bⁿ can only be true when m = n.
x = 4 -
5 Check\begin{aligned}x = 4:\quad 32 = 32\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 4 | 32 | 32 | ✓ |
Open this problem in the solver
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.