Algebra Examples

$5^{2 x - 7} = 5^{2 x + 4}$

Step 1

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

$5^{2 x - 7} = 5^{2 x + 4}$

Step 2

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

$2 x - 7 = 2 x + 4$

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 $2 x$ from both sides of the equation.

$2 x - 7 - 2 x = 4$

Step 3.1.2

Combine the opposite terms in $2 x - 7 - 2 x$ .

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Step 3.1.2.1

Subtract $2 x$ from $2 x$ .

$0 - 7 = 4$

Step 3.1.2.2

Subtract $7$ from $0$ .

$- 7 = 4$

Step 3.2

Since $- 7 \neq 4$ , there are no solutions.

No solution