Algebra Examples

$3 \cdot 10^{2 y} = 3600$

Step 1

Divide each term in $3 \cdot 10^{2 y} = 3600$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 \cdot 10^{2 y} = 3600$ by $3$ .

$\frac{3 \cdot 10^{2 y}}{3} = \frac{3600}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 \cdot 10^{2 y}}{3} = \frac{3600}{3}$

Step 1.2.1.2

Divide $10^{2 y}$ by $1$ .

$10^{2 y} = \frac{3600}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $3600$ by $3$ .

$10^{2 y} = 1200$

Step 2

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{2 y}) = \log (1200)$

Step 3

Expand the left side.

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Step 3.1

Expand $\log (10^{2 y})$ by moving $2 y$ outside the logarithm.

$2 y \log (10) = \log (1200)$

Step 3.2

Logarithm base $10$ of $10$ is $1$ .

$2 y \cdot 1 = \log (1200)$

Step 3.3

Multiply $2$ by $1$ .

$2 y = \log (1200)$

Step 4

Divide each term in $2 y = \log (1200)$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 y = \log (1200)$ by $2$ .

$\frac{2 y}{2} = \frac{\log (1200)}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\log (1200)}{2}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{\log (1200)}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{\log (1200)}{2}$

Decimal Form:

$y = 1.53959062 \dots$