Math Problem Statement

Nilai dari log₂ (1/128) adalah...

Solution

The question in the image asks for the value of:

log2(1128)\log_2 \left( \frac{1}{128} \right)

To solve this, we use the logarithmic properties and powers of 2.

Step 1: Express 1128\frac{1}{128} as a power of 2

We know that: 128=27128 = 2^7 Thus, 1128=27\frac{1}{128} = 2^{-7}

Step 2: Apply the logarithmic rule

Using the property logb(ac)=clogb(a)\log_b (a^c) = c \log_b (a), we get: log2(27)=7\log_2 \left( 2^{-7} \right) = -7

Final Answer:

The value of log2(1128)\log_2 \left( \frac{1}{128} \right) is 7-7.

Therefore, the correct answer is C. -7.

Do you need any further details or have any other questions?

Related questions:

  1. What is the general formula for calculating logarithms of fractions?
  2. How can you solve log3(181)\log_3 \left( \frac{1}{81} \right)?
  3. What is the relationship between logarithms and exponents?
  4. How would you approach log5(125)\log_5 \left( \frac{1}{25} \right)?
  5. Can you explain the change of base formula for logarithms?

Tip:

When working with logarithms, remember that fractions can often be expressed as negative exponents, which makes logarithmic calculations simpler.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

log_b (a^c) = c log_b (a)

Theorems

Logarithm properties
Power rule for logarithms

Suitable Grade Level

Grades 9-12