Solve for y 3*10^(2y)=3600

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

Step 1

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

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.

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

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

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

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

Multiply $2$ by $1$ .

$2 y = \log (1200)$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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:

$y = 1.53959062 \dots$