Precalculus Examples

$3 (2^{3 x - 1}) + 5 = 101$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$3 \cdot 2^{3 x - 1} = 101 - 5$

Step 1.2

Subtract $5$ from $101$ .

$3 \cdot 2^{3 x - 1} = 96$

Step 2

Divide each term in $3 \cdot 2^{3 x - 1} = 96$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 \cdot 2^{3 x - 1} = 96$ by $3$ .

$\frac{3 \cdot 2^{3 x - 1}}{3} = \frac{96}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 \cdot 2^{3 x - 1}}{3} = \frac{96}{3}$

Step 2.2.1.2

Divide $2^{3 x - 1}$ by $1$ .

$2^{3 x - 1} = \frac{96}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $96$ by $3$ .

$2^{3 x - 1} = 32$

Step 3

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

$2^{3 x - 1} = 2^{5}$

Step 4

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

$3 x - 1 = 5$

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 $1$ to both sides of the equation.

$3 x = 5 + 1$

Step 5.1.2

Add $5$ and $1$ .

$3 x = 6$

Step 5.2

Divide each term in $3 x = 6$ by $3$ and simplify.

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Step 5.2.1

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $3$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $6$ by $3$ .

$x = 2$