core: 3.5/10 Answered: 4/10 Question 5 Find the solution of the exponential equation e^3x+4=6 The exact solution is: a = x=square The approximate solution correct to four decimal places is x= x=square

To solve the exponential equation $e^{3x+4}=6$, we can take the natural logarithm of both sides to get rid of the exponential term.<br /><br />Taking the natural logarithm of both sides, we have:<br /><br />$\ln(e^{3x+4}) = \ln(6)$<br /><br />Using the property of logarithms that $\ln(e^y) = y$, we can simplify the left side:<br /><br />$3x+4 = \ln(6)$<br /><br />Now, we can solve for $x$ by isolating it on one side of the equation:<br /><br />$3x = \ln(6) - 4$<br /><br />$x = \frac{\ln(6) - 4}{3}$<br /><br />This is the exact solution for $x$.<br /><br />To find the approximate solution correct to four decimal places, we can evaluate the expression using a calculator:<br /><br />$x \approx \frac{\ln(6) - 4}{3} \approx -0.5347$<br /><br />Therefore, the exact solution is $x = \frac{\ln(6) - 4}{3}$ and the approximate solution correct to four decimal places is $x \approx -0.5347$.