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Let f(x)=33x+1752x.f(x)=3^{3 x+1}-7 \cdot 5^{2 x}. a. Use the Maple commands solve and ff solve to try to find all roots of f.f. b. Plot f(x)f(x) to find initial approximations to roots of f.f. c. Use Newton’s method to find roots of ff to within 101610^{-16} d. Find the exact solutions of f(x)=0f(x)=0 without using Maple.

Solution

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Answered 2 months ago
Answered 2 months ago

Apply the function solve\texttt{solve} in Maple as follows. The first argument is the equation we are trying to solve, the second one is the variable.

solve(3^(3*x+1)-7*5^(2*x)=0, x)

The result we get is

ln3ln73ln32ln5-\dfrac{\ln{3}-\ln{7}}{3\ln{3}-2\ln{5}}

Evaluate the expression to obtain the solution

x=11.0094386x=11.0094386

The function fsolve is applied a bit differently, as shown below. The solution we get is the same as before.

f := 3^(3*x + 1) - 7*5^(2*x) = 0;
fsolve(f);
                          11.00943864

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