Algebra Examples

$2 \cdot 4^{3 x - 6} - 8 = 120$

Step 1

Multiply $2 \cdot 4^{3 x - 6}$ .

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$2 \cdot {(2^{2})}^{3 x - 6} - 8 = 120$

Step 1.2

Multiply the exponents in ${(2^{2})}^{3 x - 6}$ .

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Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{2 (3 x - 6)} - 8 = 120$

Step 1.2.2

Apply the distributive property.

$2 \cdot 2^{2 (3 x) + 2 \cdot - 6} - 8 = 120$

Step 1.2.3

Multiply $3$ by $2$ .

$2 \cdot 2^{6 x + 2 \cdot - 6} - 8 = 120$

Step 1.2.4

Multiply $2$ by $- 6$ .

$2 \cdot 2^{6 x - 12} - 8 = 120$

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{1 + 6 x - 12} - 8 = 120$

Step 1.4

Subtract $12$ from $1$ .

$2^{6 x - 11} - 8 = 120$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $8$ to both sides of the equation.

$2^{6 x - 11} = 120 + 8$

Step 2.2

Add $120$ and $8$ .

$2^{6 x - 11} = 128$

Step 3

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

$2^{6 x - 11} = 2^{7}$

Step 4

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

$6 x - 11 = 7$

Step 5

Solve for $x$ .

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Step 5.1

Move all terms not containing $x$ to the right side of the equation.

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Step 5.1.1

Add $11$ to both sides of the equation.

$6 x = 7 + 11$

Step 5.1.2

Add $7$ and $11$ .

$6 x = 18$

Step 5.2

Divide each term in $6 x = 18$ by $6$ and simplify.

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Step 5.2.1

Divide each term in $6 x = 18$ by $6$ .

$\frac{6 x}{6} = \frac{18}{6}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $6$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{18}{6}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{6}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $18$ by $6$ .

$x = 3$