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We want to solve the following equation.

sqrt(3x+3)=e^(x)
One of the solutions is
x~~-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. $\newline$ $\sqrt{3 x+3}=e^{x}$ $\newline$ One of the solutions is $x \approx-1$ . $\newline$ 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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Change of base formula

Full solution

Q. We want to solve the following equation.

\newline

\sqrt{3 x+3}=e^{x}

\newline

One of the solutions is

x \approx-1

.

\newline

Find the other solution.

\newline

Hint: Use a graphing calculator.

\newline

Round your answer to the nearest tenth.

\newline

x \approx

Set Up Equation: First, we need to set up the equation that we are trying to solve: $\sqrt{3x+3} = e^{x}$
Graph Functions: Since we are given a hint to use a graphing calculator, we will graph both sides of the equation as separate functions and look for their points of intersection. $\newline$ Function $1$ : $y = \sqrt{3x+3}$ $\newline$ Function $2$ : $y = e^{x}$
Find Intersection: Using a graphing calculator, we plot both functions on the same set of axes. We already know that one intersection point is around $x = -1$ . We are looking for the other point where the two graphs intersect.
Calculate Solution: After graphing, we find the other point of intersection by using the calculator's intersection feature or by visually inspecting the graph for the approximate value of $x$ where the two functions meet.
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for $x$ and round it to the nearest tenth as instructed. $\newline$ Let's say the calculator gives us an intersection at $x = 1.5$ (this is a hypothetical value for the purpose of this example).
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for $x$ and round it to the nearest tenth as instructed. $\newline$ Let's say the calculator gives us an intersection at $x = 1.5$ (this is a hypothetical value for the purpose of this example).We check our solution by plugging it back into the original equation to see if both sides are approximately equal. $\newline$ $\sqrt{3*1.5+3}$ ?= $e^{1.5}$ $\newline$ $\sqrt{4.5+3}$ ?= $e^{1.5}$ $\newline$ $\sqrt{7.5}$ ?= $e^{1.5}$
Verify Solution: Assuming no mistakes were made in using the graphing calculator, we find the other solution for $x$ and round it to the nearest tenth as instructed. $\newline$ Let's say the calculator gives us an intersection at $x = 1.5$ (this is a hypothetical value for the purpose of this example).We check our solution by plugging it back into the original equation to see if both sides are approximately equal. $\newline$ $\sqrt{3*1.5+3}$ ?= $e^{1.5}$ $\newline$ $\sqrt{4.5+3}$ ?= $e^{1.5}$ $\newline$ $\sqrt{7.5}$ ?= $e^{1.5}$ We use a calculator to find the numerical values of both sides to verify the solution. $\newline$ $\sqrt{7.5} \approx 2.74$ $\newline$ $e^{1.5} \approx 4.48$ $\newline$ Since these values are not approximately equal, we realize there has been a mistake in our calculation or in reading the graphing calculator's output.

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