Question

submitting an external toolial equation.
$3^{2x - 3}=5^{4x + 5}$places and do not include \$x=$\ in your answer.ver below:

Explanation:

Step1: Take the natural logarithm of both sides

$$\ln(3^{2x - 3})=\ln(5^{4x + 5})$$
Using the property $\ln(a^b)=b\ln(a)$, we get $(2x - 3)\ln(3)=(4x + 5)\ln(5)$.

Step2: Expand the equation

$$2x\ln(3)-3\ln(3)=4x\ln(5)+5\ln(5)$$

Step3: Group the x - terms

$$2x\ln(3)-4x\ln(5)=5\ln(5)+3\ln(3)$$
Factor out x: $x(2\ln(3)-4\ln(5))=5\ln(5)+3\ln(3)$.

Step4: Solve for x

$$x=\frac{5\ln(5)+3\ln(3)}{2\ln(3)-4\ln(5)}$$
Now, using a calculator:
$\ln(3)\approx1.0986$, $\ln(5)\approx1.6094$
$$x=\frac{5\times1.6094 + 3\times1.0986}{2\times1.0986-4\times1.6094}$$
$$x=\frac{8.047+3.2958}{2.1972 - 6.4376}$$
$$x=\frac{11.3428}{-4.2404}\approx - 2.675$$

Answer:

$-2.675$