Solve the Inequality for x 4^(2x+3)=1

$4^{2 x + 3} = 1$

Step 1

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

$\ln (4^{2 x + 3}) = \ln (1)$

Step 2

Expand $\ln (4^{2 x + 3})$ by moving $2 x + 3$ outside the logarithm.

$(2 x + 3) \ln (4) = \ln (1)$

Step 3

Simplify the left side.

Apply the distributive property.

$2 x \ln (4) + 3 \ln (4) = \ln (1)$

Step 4

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$2 x \ln (4) + 3 \ln (4) = 0$

Step 5

Subtract $3 \ln (4)$ from both sides of the equation.

$2 x \ln (4) = - 3 \ln (4)$

Step 6

Divide each term in $2 x \ln (4) = - 3 \ln (4)$ by $2 \ln (4)$ and simplify.

Divide each term in $2 x \ln (4) = - 3 \ln (4)$ by $2 \ln (4)$ .

$\frac{2 x \ln (4)}{2 \ln (4)} = \frac{- 3 \ln (4)}{2 \ln (4)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (4)}{2 \ln (4)} = \frac{- 3 \ln (4)}{2 \ln (4)}$

Rewrite the expression.

$\frac{x \ln (4)}{\ln (4)} = \frac{- 3 \ln (4)}{2 \ln (4)}$

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{- 3 \ln (4)}{2 \ln (4)}$

Divide $x$ by $1$ .

$x = \frac{- 3 \ln (4)}{2 \ln (4)}$

Simplify the right side.

Cancel the common factor of $\ln (4)$ .

Cancel the common factor.

$x = \frac{- 3 \ln (4)}{2 \ln (4)}$

Rewrite the expression.

$x = \frac{- 3}{2}$

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{2}$

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$

Solve the Inequality for x 4^(2x+3)=1

Related Questions

Support LCMGCF.com by disabling your adblocker.