Calculus Examples

$10^{x + 4} = 100^{x}$

Step 1

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

$10^{x + 4} = 10^{2 x}$

Step 2

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

$x + 4 = 2 x$

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.

$x + 4 - 2 x = 0$

Step 3.1.2

Subtract $2 x$ from $x$ .

$- x + 4 = 0$

Step 3.2

Subtract $4$ from both sides of the equation.

$- x = - 4$

Step 3.3

Divide each term in $- x = - 4$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 4$ by $- 1$ .

$x = 4$