Algebra Examples

$3^{x + 1} = 3^{x - 7}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$3^{x + 1} = 3^{x - 7}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x + 1 = x - 7$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$x + 1 - x = - 7$

Step 3.1.2

Combine the opposite terms in $x + 1 - x$ .

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Step 3.1.2.1

Subtract $x$ from $x$ .

$0 + 1 = - 7$

Step 3.1.2.2

Add $0$ and $1$ .

$1 = - 7$

Step 3.2

Since $1 \neq - 7$ , there are no solutions.

No solution