question\nsolve for $x$, rounding to the nearest hundredth.\n$56e^{4x}=90$

Answer:

$x \approx 0.11$

Explanation:

Step1: Isolate the exponential term

Divide both sides by 56: $$e^{4x} = \frac{90}{56}$$ Simplify the fraction: $$e^{4x} = \frac{45}{28} \approx 1.6071$$

Step2: Apply natural logarithm

Take $\ln$ of both sides: $$\ln\left(e^{4x}\right) = \ln\left(\frac{45}{28}\right)$$ Use $\ln(e^a)=a$: $$4x = \ln\left(\frac{45}{28}\right)$$

Step3: Solve for x

Divide both sides by 4: $$x = \frac{\ln\left(\frac{45}{28}\right)}{4}$$ Calculate the value: $$x \approx \frac{0.4700}{4} \approx 0.11$$