Solve for x 1.2=3^(2x)-3

$1.2 = 3^{2 x} - 3$

Rewrite the equation as $3^{2 x} - 3 = 1.2$ .

$3^{2 x} - 3 = 1.2$

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

Add $3$ to both sides of the equation.

$3^{2 x} = 1.2 + 3$

Add $1.2$ and $3$ .

$3^{2 x} = 4.2$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (3^{2 x}) = \ln (4.2)$

Expand $\ln (3^{2 x})$ by moving $2 x$ outside the logarithm.

$2 x \ln (3) = \ln (4.2)$

Divide each term in $2 x \ln (3) = \ln (4.2)$ by $2 \ln (3)$ and simplify.

Divide each term in $2 x \ln (3) = \ln (4.2)$ by $2 \ln (3)$ .

$\frac{2 x \ln (3)}{2 \ln (3)} = \frac{\ln (4.2)}{2 \ln (3)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (3)}{2 \ln (3)} = \frac{\ln (4.2)}{2 \ln (3)}$

Rewrite the expression.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4.2)}{2 \ln (3)}$

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4.2)}{2 \ln (3)}$

Divide $x$ by $1$ .

$x = \frac{\ln (4.2)}{2 \ln (3)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (4.2)}{2 \ln (3)}$

Decimal Form:

$x = 0.65313511 \dots$