Logarithmic and Exponential Equations Score: 4/10 Answered: 5/10 square Solve the equation ln(6x+5)=2 The exact solution (using exponents) is z = x=square The solution, rounded to 4 decimal places is z= Question Help: Video (1) Message instructor

To solve the equation $ln(6x+5)=2$, we need to isolate the variable $x$.<br /><br />Step 1: Rewrite the equation in exponential form.<br />$e^{ln(6x+5)}=e^2$<br />$6x+5=e^2$<br /><br />Step 2: Subtract 5 from both sides of the equation.<br />$6x=e^2-5$<br /><br />Step 3: Divide both sides of the equation by 6.<br />$x=\frac{e^2-5}{6}$<br /><br />Therefore, the exact solution is $x=\frac{e^2-5}{6}$.<br /><br />To find the solution rounded to 4 decimal places, we can use a calculator to evaluate the expression $\frac{e^2-5}{6}$.<br /><br />Using a calculator, we find that $\frac{e^2-5}{6} \approx 0.6481$.<br /><br />Therefore, the solution rounded to 4 decimal places is $x \approx 0.6481$.