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We want to solve the following equation.

4x^(2)-16 x+13=3log_(2)(x)
One of the solutions is
x~~1.1.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.

x~~

We want to solve the following equation. $\newline$ $4 x^{2}-16 x+13=3 \log _{2}(x)$ $\newline$ One of the solutions is $x \approx 1.1$ . $\newline$ Find the other solution. $\newline$ Hint: Use a graphing calculator. $\newline$ Round your answer to the nearest tenth. $\newline$ $x \approx$

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Scale drawings: word problems

Full solution

Q. We want to solve the following equation.

\newline

4 x^{2}-16 x+13=3 \log _{2}(x)

\newline

One of the solutions is

x \approx 1.1

.

\newline

Find the other solution.

\newline

Hint: Use a graphing calculator.

\newline

Round your answer to the nearest tenth.

\newline

x \approx

Understanding the Equation: First, we need to understand that the equation given is a transcendental equation because it involves both a polynomial and a logarithmic function. To find the solution, we will use a graphing calculator to plot both sides of the equation as separate functions and look for their points of intersection. $\newline$ Let's define two functions: $\newline$ $f(x) = 4x^2 - 16x + 13$ $\newline$ $g(x) = 3\log_2(x)$ $\newline$ We are given that one solution is approximately $x \approx 1.1$ . We need to find the other solution.
Defining the Functions: Using a graphing calculator, we plot the two functions $f(x)$ and $g(x)$ on the same set of axes. We look for the points where the graphs intersect, which represent the solutions to the original equation.
Plotting the Functions: After plotting the functions, we find that there are two points of intersection. One is near $x \approx 1.1$ , which we already know. The other intersection point will give us the second solution to the equation.
Finding the Intersection Points: Using the graphing calculator's function to find the intersection point, we can determine the $x$ -coordinate of the second point of intersection, which is the other solution to the equation.
Determining the Second Solution: The graphing calculator gives us the $x$ -coordinate of the second intersection point. We round this value to the nearest tenth to get our final answer.

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