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It is given that $\log_8 = 1.893$, correct to 3 decimal places - HSC - SSCE Mathematics Extension 1 - Question 2 - 2017 - Paper 1

Question 2

$It-is-given-that-$\log_8-=-1.893$,-correct-to-3-decimal-places-HSC-SSCE Mathematics Extension 1-Question 2-2017-Paper 1.png$

It is given that $\log_8 = 1.893$, correct to 3 decimal places. What is the value of $\log_4$, correct to 2 decimal places? A. 0.95 B. 1.26 C. 1.53 D. 2.84

Worked Solution & Example Answer:It is given that $\log_8 = 1.893$, correct to 3 decimal places - HSC - SSCE Mathematics Extension 1 - Question 2 - 2017 - Paper 1

Step 1

Given log properties

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Answer

We know that:

$\log_8 = \frac{\log_2}{\log_8} = \frac{\log_4}{\log_4}$

Using the change of base formula for logarithms, we have:

$\log_4 = \frac{\log_8}{\log_4}$ which can be expressed using the known value of $\log_8$ .

Step 2

Finding log base conversion

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Answer

Using the relationship between logarithms:

Step 1

We know that: $\log_4 = \frac{\log_8}{\log_2}\times \log_4$

Step 2

Assuming $\log_2 = 3 \log_4$ , we substitute: $\log_4 = 1.893 \div (3/2) = 1.26$

Step 3

Final answer

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Answer

Thus, the value of $\log_4$ , correct to 2 decimal places, is:

1.26 which corresponds to option B.

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