Algebra Examples

$1000^{1000} = 100^{x}$

Step 1

Rewrite the equation as $100^{x} = 1000^{1000}$ .

$100^{x} = 1000^{1000}$

Step 2

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

$10^{2 x} = 10^{3 \cdot 1000}$

Step 3

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

$2 x = 3 \cdot 1000$

Step 4

Solve for $x$ .

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Step 4.1

Multiply $3$ by $1000$ .

$2 x = 3000$

Step 4.2

Divide each term in $2 x = 3000$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 x = 3000$ by $2$ .

$\frac{2 x}{2} = \frac{3000}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3000}{2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3000}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $3000$ by $2$ .

$x = 1500$