Question

Select the correct answer to the following equation: 27x3/4−1=26
.(1 point)
Responses

2527
Start Fraction 25 over 27 End Fraction

1
1

0
0

3

Answer 1

To solve the equation \( 27^{x \frac{3}{4}} - 1 = 26 \), we can first simplify it:

1. Add 1 to both sides:
\[
27^{x \frac{3}{4}} = 27
\]

2. Since \( 27 \) can be expressed as \( 27^1 \), we have:
\[
27^{x \frac{3}{4}} = 27^1
\]

3. Since the bases are the same, we can set the exponents equal to each other:
\[
x \frac{3}{4} = 1
\]

4. To solve for \( x \), multiply both sides by \( \frac{4}{3} \):
\[
x = \frac{4}{3}
\]

Now we evaluate \( x \) with respect to the given answer choices:

- **2527** - not relevant
- **Start Fraction 25 over 27 End Fraction** - not relevant
- **1** - not relevant
- **0** - not relevant
- **3** - not correct

Since \( x = \frac{4}{3} \) does not match any of the provided options directly, it seems there may be some error in the choices or in my interpretation. However, if we evaluate what could be the closest approximation, none of these options apply.

Concluding, it appears there are no correct answers matching the solution presented. But the algebraic solution for the original equation yields \( x = \frac{4}{3} \).