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Question

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Find the value of the logarithms without using a calculator.
a.
log Subscript 2 Baseline 16
b.
log Subscript 7 Baseline 49
c.
log Subscript 4 Baseline 64
d.
log Subscript 3 Baseline 27
e.
log Subscript 6 Baseline 216
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Part 1
a. log Subscript 2 Baseline 16equals
  
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Answer 1

To solve the logarithmic problems, we can use the definition of logarithms. The logarithm \( \log_b(a) = c \) means that \( b^c = a \).

Let’s solve each one:

a. \( \log_2(16) \)

We know that \( 16 = 2^4 \). Therefore, \( \log_2(16) = 4 \).

b. \( \log_7(49) \)

We know that \( 49 = 7^2 \). Therefore, \( \log_7(49) = 2 \).

c. \( \log_4(64) \)

We can express \( 64 \) as \( 4^3 \) since \( 4 = 2^2 \) and \( 64 = 2^6 \). Thus, \[ \log_4(64) = \log_4(4^3) = 3 \].

d. \( \log_3(27) \)

We know that \( 27 = 3^3 \). Therefore, \( \log_3(27) = 3 \).

e. \( \log_6(216) \)

We know that \( 216 = 6^3 \). Therefore, \( \log_6(216) = 3 \).

Here are the results:

a. \( \log_2(16) = 4 \)
b. \( \log_7(49) = 2 \)
c. \( \log_4(64) = 3 \)
d. \( \log_3(27) = 3 \)
e. \( \log_6(216) = 3 \)

Please let me know if you need further assistance!