Question

o solve the equation \( (3 exponent 3)^x = 3 exponent24 \),

Answer 1

u sure

Answer 2

To solve the equation \( (3^3)^x = 3^{24} \), we start by simplifying the left side. We can apply the power of a power rule of exponents, which states that \( (a^m)^n = a^{m \cdot n} \). Thus, we have:

\[
(3^3)^x = 3^{3x}
\]

Now we can rewrite the equation as:

\[
3^{3x} = 3^{24}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
3x = 24
\]

Next, we solve for \( x \) by dividing both sides of the equation by 3:

\[
x = \frac{24}{3}
\]
\[
x = 8
\]

Thus, the solution to the equation is

\[
\boxed{8}
\]

Answer 3

Yes, I am sure about the solution. Let's recap the steps to verify that everything is correct.

Starting with the original equation:

\[
(3^3)^x = 3^{24}
\]

We apply the power of a power property of exponents:

\[
(3^3)^x = 3^{3x}
\]

So the equation can be rewritten as:

\[
3^{3x} = 3^{24}
\]

Since the bases (3) are the same, we set the exponents equal to each other:

\[
3x = 24
\]

We solve for \( x \) by dividing both sides by 3:

\[
x = \frac{24}{3} = 8
\]

Thus, the final solution is:

\[
\boxed{8}
\]

Everything checks out correctly! If you have any further questions or need more clarification, feel free to ask.