Question

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

0
0

25/27
Start Fraction 25 over 27 End Fraction

3
3

1

Answer 1

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

1. Isolate the term with the exponent:
\[
27^{x \frac{3}{4}} = 26 + 1 = 27
\]

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

3. This implies:
\[
3x \frac{3}{4} = 3
\]

4. Divide both sides by 3:
\[
x \frac{3}{4} = 1
\]

5. Multiply both sides by \( \frac{4}{3} \):
\[
x = \frac{4}{3}
\]

None of the provided options correspond to \( \frac{4}{3} \), suggesting an error in the assumptions or the options provided. Let's check if we made any calculation errors.

Since \( 27^{x \frac{3}{4}} = 27 \) directly implies \( x \frac{3}{4} = 1 \) indeed gives \( x = \frac{4}{3} \).

Assuming that the options provided might represent a misunderstanding of the fractions, the only fraction approaching a solution from \( 0, \frac{25}{27}, 3, 1 \) doesn’t apply.

Therefore, the answer to \( 27^{x \frac{3}{4}} = 27 \) leads us clearly to \( x = \frac{4}{3} \), which is unfortunately not one of the provided options.

Please verify the question for correctness or option listings. However, based on the direct calculation:

The correct value for \(x\) based on solving is \( \frac{4}{3} \).