Question

Match the exponential equation to the correct answer.

5^27=5^−9x
3^x−4+2x=3^3(2x+7)
12^x−5=12^3x

Answer 1

Sure! Let's solve each exponential equation step by step to find the correct answers.

1. **Equation: \(5^{27} = 5^{-9x}\)**

Since the bases are the same, we can equate the exponents:
\[
27 = -9x
\]
To solve for \(x\), divide both sides by \(-9\):
\[
x = \frac{27}{-9} = -3
\]

2. **Equation: \(3^{x-4} + 2x = 3^{3}(2x + 7)\)**

Start by simplifying the right side:
\[
3^3 = 27
\]
Therefore:
\[
27(2x + 7) = 54x + 189
\]
Now, rewrite the equation:
\[
3^{x-4} + 2x = 54x + 189
\]
Rearranging gives:
\[
3^{x-4} = 52x + 189
\]
This equation may need numerical or graphical methods to solve, as it is not straightforward to isolate \(x\).

3. **Equation: \(12^{x-5} = 12^{3x}\)**

Again, since the bases are the same, we equate the exponents:
\[
x - 5 = 3x
\]
Rearranging gives:
\[
-5 = 2x
\]
Thus:
\[
x = -\frac{5}{2} = -2.5
\]

So far, we have the following solutions:

- For \(5^{27} = 5^{-9x}\), the solution is \(x = -3\).
- The equation \(3^{x-4} + 2x = 3^{3}(2x + 7)\) needs further numerical or graphical exploration or a specific value to be solved correctly.
- For \(12^{x-5} = 12^{3x}\), the solution is \(x = -2.5\).

If you provide specific options to match, we can proceed to identify which match these calculations!