a. Find an equation of the tangent line at $x=a$. b. Use a graphing utility to graph the curve and the tangent line on the same set of axes. \[ y=e^{x} ; a=\ln 10 \] a. At $x=a$, an equation of the tangent line is $y=$

Step 1 ：We are given the function \(y=e^{x}\) and \(a=\ln 10\).

Step 2 ：The equation of the tangent line to the function \(f(x)\) at \(x=a\) is given by \(y=f(a)+f'(a)(x-a)\).

Step 3 ：First, we need to find the value of \(f(a)\) and \(f'(a)\).

Step 4 ：Since \(f(x)=e^{x}\), we have \(f(a)=e^{\ln 10}=10\).

Step 5 ：The derivative of \(f(x)=e^{x}\) is also \(e^{x}\), so \(f'(a)=e^{\ln 10}=10\).

Step 6 ：Substituting these values into the equation of the tangent line, we get \(y=10+10(x-\ln 10)\).

Step 7 ：Simplifying this equation, we get \(y=10x-13.02585092994046\).

Step 8 ：\(\boxed{y=10x-13.02585092994046}\) is the equation of the tangent line at \(x=a\).