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Gr 10 Math Ch 2: Exponential Equations

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Questions and Answers

What can be concluded if the equation is structured as $5^x = 5^3$?

$x = 8$

$x = 5$

$x = 3$ (correct)

$x = 0$

Which method is appropriate for solving the equation $2^x = 3^x$?

Setting x equal to 0

Using logarithms to isolate the exponent (correct)

Factoring both sides

Equating the bases directly

What is the first step to solve the equation $4^x = 16$?

Express 16 as $4^2$ (correct)

Isolate x by dividing both sides by 4

Check for extraneous solutions

Raise both sides to the power of x

After solving an exponential equation, why is it necessary to check for extraneous solutions?

To verify solutions align with the original equation Signup and view all the answers

If you have the equation $e^{2x} = e^{3x - 1}$, what is the next step after applying logarithms?

Set $2x$ equal to $3x - 1$ Signup and view all the answers

What can be inferred about the solution of the equation $7^x = 7^5$?

The solution is $x = 5$. Signup and view all the answers

If an exponential equation cannot be simplified to have the same base, which method should be used?

Using logarithms. Signup and view all the answers

In the process of solving $10^{2x} = 1000$, what is the first step taken?

Rewriting $1000$ as $10^3$. Signup and view all the answers

When solving the equation $3^x = 27$, what should you do after confirming that both sides can be expressed with the same base?

Set the exponents equal to solve for $x$. Signup and view all the answers

What step is necessary after finding a solution to an exponential equation?

Check the solution in the original equation. Signup and view all the answers

Which statement about the equation $a^x = a^y$ is true given that $a > 0$ and $a \neq 1$?

The relationship $x = y$ holds true. Signup and view all the answers

When the equation is written as $4^x = 64$, what is the next suitable step?

Change 64 to $4^3$ and set exponents equal. Signup and view all the answers

If both sides of an exponential equation cannot be expressed with the same base, what is the primary strategy to use?

Employ logarithms to isolate the exponent. Signup and view all the answers

Which of the following correctly describes extraneous solutions?

They must be checked against the original equation to confirm legitimacy. Signup and view all the answers

What should be done after finding a solution to the equation $2^x = 8$?

Confirm the solution by substituting it back into the original equation. Signup and view all the answers