We read your photo as:

Rewrite the constant term '1' as a logarithm with base 2.

Chemistry

ScanSolve AI Answer

Answer

x=2y2−1x = 2y^2 - 1

Step-by-step solution

6 steps

  1. Rewrite the constant term '1' as a logarithm with base 2.

    We know that log⁡bb=1\log_b b = 1. Therefore, 1=log⁡221 = \log_2 2.

  2. Substitute this into the original equation.

    log⁡2(x+1)−log⁡22=2log⁡2y\log_2(x+1) - \log_2 2 = 2 \log_2 y

  3. Apply the logarithm property log⁡bA−log⁡bB=log⁡b(AB)\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right) to the left side of the equation.

    log⁡2(x+12)=2log⁡2y\log_2 \left(\frac{x+1}{2}\right) = 2 \log_2 y

  4. Apply the logarithm property clog⁡bA=log⁡b(Ac)c \log_b A = \log_b (A^c) to the right side of the equation.

    log⁡2(x+12)=log⁡2(y2)\log_2 \left(\frac{x+1}{2}\right) = \log_2 (y^2)

  5. Since the logarithms on both sides have the same base, their arguments must be equal.

    x+12=y2\frac{x+1}{2} = y^2

  6. Solve for xx in terms of yy.

    x+1=2y2x+1 = 2y^2 x=2y2−1x = 2y^2 - 1

    The solution expresses xx in terms of yy.

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 Chemistry Questions

QRewrite the base and argument of the logarithm with a common base.QConvert all logarithms to a common base, which is base 2.QRewrite the expression using logarithm properties.QRewrite the expression inside the logarithm in terms of base 3.QExpress as a single logarithm:
See all Chemistry 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