We read your photo as:

(0.25)^x−1 = 32

Mathematics

ScanSolve AI Answer

Answer

−32-\frac{3}{2}

Step-by-step solution

6 steps

  1. Convert the decimal 0.25 to a fraction and express it as a power of 2.

    0.25=14=122=2−20.25 = \frac{1}{4} = \frac{1}{2^2} = 2^{-2}

  2. Express 32 as a power of 2.

    32=2532 = 2^5

  3. Substitute these into the given equation.

    (2−2)x−1=25(2^{-2})^{x-1} = 2^5

  4. Apply the exponent rule (am)n=amn(a^m)^n = a^{mn} to the left side of the equation.

    2−2(x−1)=252^{-2(x-1)} = 2^5 2−2x+2=252^{-2x+2} = 2^5

  5. Since the bases are equal, equate the exponents.

    −2x+2=5-2x+2 = 5

  6. Solve the linear equation for xx.

    −2x=5−2-2x = 5 - 2 −2x=3-2x = 3 x=−32x = -\frac{3}{2}

    The value of xx is −32\boxed{-\frac{3}{2}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSolve for x in the following equations: (i) (0.25)^x+1 = 16QSolve for x in 16^x+1 = 0.25QSolve for x: (2x−1)2 = 25QSolve for x: 5^(x+2) = 1/25 and 27.3^x = 1QSolve for x in the equations: 3.3.2 5^(x+2) = 1/25 and 3.3.1 27.3^x = 1
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp