We read your photo as:

Simplify the expression: (1)/(2)3 36 - 3 2 - 33 3

Mathematics

ScanSolve AI Answer

Answer

-2

Step-by-step solution

7 steps

  1. Apply the power rule of logarithms, clog⁡bM=log⁡b(Mc)c \log_b M = \log_b (M^c), to each term.

    12log⁡336=log⁡3(361/2)=log⁡336=log⁡36\frac{1}{2}\log_3 36 = \log_3 (36^{1/2}) = \log_3 \sqrt{36} = \log_3 6 3log⁡33=log⁡3(33)=log⁡3273\log_3 3 = \log_3 (3^3) = \log_3 27

  2. Substitute these simplified terms back into the original expression.

    log⁡36−log⁡32−log⁡327\log_3 6 - \log_3 2 - \log_3 27

  3. Apply the quotient rule of logarithms, log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right), from left to right.

    First, combine the first two terms:

    log⁡36−log⁡32=log⁡3(62)=log⁡33\log_3 6 - \log_3 2 = \log_3 \left(\frac{6}{2}\right) = \log_3 3

  4. Combine the result with the third term.

    log⁡33−log⁡327=log⁡3(327)\log_3 3 - \log_3 27 = \log_3 \left(\frac{3}{27}\right)

  5. Simplify the fraction inside the logarithm.

    log⁡3(19)\log_3 \left(\frac{1}{9}\right)

  6. Express 19\frac{1}{9} as a power of 3.

    Since 9=329 = 3^2, then 19=3−2\frac{1}{9} = 3^{-2}.

    log⁡3(3−2)\log_3 (3^{-2})

  7. Use the definition of logarithm, log⁡b(bx)=x\log_b (b^x) = x.

    log⁡3(3−2)=−2\log_3 (3^{-2}) = -2

    The simplified expression is:

    −2-2
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

QSimplify the following expression: ((32)/(3) of 21 + 3(3)/(4) / (3)/(8) − 4(1)/(2)…QSimplify the expression: (3)/(x+1) − (2)/(x+2)
Browse by topic:Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.