We read your photo as:

Evaluate the first logarithm term, 64 256.

Mathematics

ScanSolve AI Answer

Answer

C) 2\text{C) 2}

Step-by-step solution

4 steps

C) 2

  1. Evaluate the first logarithm term, 64log⁡256^{64}\log 256.

    We can express both the base and the argument as powers of 2.
    64=2664 = 2^6 and 256=28256 = 2^8.
    Using the logarithm property log⁡bman=nmlog⁡ba\log_{b^m} a^n = \frac{n}{m} \log_b a:

    64log⁡256=log⁡2628=86log⁡22^{64}\log 256 = \log_{2^6} 2^8 = \frac{8}{6} \log_2 2

    Since log⁡22=1\log_2 2 = 1:

    64log⁡256=86×1=43^{64}\log 256 = \frac{8}{6} \times 1 = \frac{4}{3}
  2. Evaluate the second logarithm term, 27log⁡9^{27}\log 9.

    We can express both the base and the argument as powers of 3.
    27=3327 = 3^3 and 9=329 = 3^2.
    Using the logarithm property log⁡bman=nmlog⁡ba\log_{b^m} a^n = \frac{n}{m} \log_b a:

    27log⁡9=log⁡3332=23log⁡33^{27}\log 9 = \log_{3^3} 3^2 = \frac{2}{3} \log_3 3

    Since log⁡33=1\log_3 3 = 1:

    27log⁡9=23×1=23^{27}\log 9 = \frac{2}{3} \times 1 = \frac{2}{3}
  3. Add the results from Step 1 and Step 2.

    43+23=4+23=63=2\frac{4}{3} + \frac{2}{3} = \frac{4+2}{3} = \frac{6}{3} = 2

    The value of the expression is 2.

  4. Compare the result with the given options.

    The calculated value is 2, which matches option C.

    The final answer is C) 2\text{C) 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
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