Algebra Examples

$64^{x + 1} = 32^{\frac{6}{5} x}$

Step 1

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

$2^{6 (x + 1)} = 2^{5 (\frac{6}{5} x)}$

Step 2

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

$6 (x + 1) = 5 (\frac{6}{5} x)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $6 (x + 1)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 6 (x + 1) = 5 (\frac{6}{5}) \cdot x$

Step 3.1.2

Simplify by adding zeros.

$6 (x + 1) = 5 (\frac{6}{5}) \cdot x$

Step 3.1.3

Apply the distributive property.

$6 x + 6 \cdot 1 = 5 (\frac{6}{5}) \cdot x$

Step 3.1.4

Multiply $6$ by $1$ .

$6 x + 6 = 5 (\frac{6}{5}) \cdot x$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Cancel the common factor.

$6 x + 6 = 5 (\frac{6}{5}) \cdot x$

Step 3.2.2

Rewrite the expression.

$6 x + 6 = 6 \cdot x$

$6 x + 6 = 6 x$

Step 3.3

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

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Step 3.3.1

Subtract $6 x$ from both sides of the equation.

$6 x + 6 - 6 x = 0$

Step 3.3.2

Combine the opposite terms in $6 x + 6 - 6 x$ .

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Step 3.3.2.1

Subtract $6 x$ from $6 x$ .

$0 + 6 = 0$

Step 3.3.2.2

Add $0$ and $6$ .

$6 = 0$

Step 3.4

Since $6 \neq 0$ , there are no solutions.

No solution