Step 1: Combine the like terms on the left side of the equation. 2^x + 2^x = 1; 2 · 2^x = 1; Step 2: Use the exponent rule a^m · aⁿ = a^(m+n) to simplify the left side. Here, 2 = 2¹. 2^(1+x) = 1 Step 3: To solve for x, we can take the logarithm of both sides. Alternatively, we know that any non-zero number raised to the power of 0 equals 1. 2^(1+x) = 2⁰ Step 4: Since the bases are the same, the exponents must be equal. 1+x = 0 Step 5: Solve for x. x = −1 The final answer is −1.

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2^x + 2^x = 1

June 29, 2026Mathematics

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Answer

-1

Step-by-step solution

5 steps

Combine the like terms on the left side of the equation.
$2^x + 2^x = 1$ $2 \cdot 2^x = 1$
Use the exponent rule $a^m \cdot a^n = a^{m+n}$ to simplify the left side.
Here, $2 = 2^1$ .
$2^{1+x} = 1$
To solve for $x$ , we can take the logarithm of both sides.
Alternatively, we know that any non-zero number raised to the power of 0 equals 1.
$2^{1+x} = 2^0$
Since the bases are the same, the exponents must be equal.
$1+x = 0$
Solve for $x$ .
$x = -1$
The final answer is $-1$ .

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2^x + 2^x = 1

Answer

Step-by-step solution

Combine the like terms on the left side of the equation.

Use the exponent rule am⋅an=am+na^m \cdot a^n = a^{m+n}am⋅an=am+n to simplify the left side.

To solve for xxx, we can take the logarithm of both sides.

Since the bases are the same, the exponents must be equal.

Solve for xxx.

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Still stuck on this one?

More Mathematics Questions

Use the exponent rule $a^m \cdot a^n = a^{m+n}$ to simplify the left side.

To solve for $x$ , we can take the logarithm of both sides.

Solve for $x$ .