Algebra Examples

$30 \cdot 5^{x + 3} = 150$

Step 1

Divide each term in $30 \cdot 5^{x + 3} = 150$ by $30$ and simplify.

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Step 1.1

Divide each term in $30 \cdot 5^{x + 3} = 150$ by $30$ .

$\frac{30 \cdot 5^{x + 3}}{30} = \frac{150}{30}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $30$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{30 \cdot 5^{x + 3}}{30} = \frac{150}{30}$

Step 1.2.1.2

Divide $5^{x + 3}$ by $1$ .

$5^{x + 3} = \frac{150}{30}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $150$ by $30$ .

$5^{x + 3} = 5$

Step 2

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

$5^{x + 3} = 5^{1}$

Step 3

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

$x + 3 = 1$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

$x = 1 - 3$

Step 4.2

Subtract $3$ from $1$ .

$x = - 2$