Answer:
- 10001
- 7
Step-by-step explanation:
You want 17 written in binary, and the value of the expression ...
3log₂(4) -2log₂(3) +log₂(18)
1. Binary
A decimal number can be converted to binary (base 2) by looking at the remainders from successive division by 2.
- 17 ÷ 2 = 8 r 1
- 8 ÷ 2 = 4 r 0
- 4 ÷ 2 = 2 r 0
- 2 ÷ 2 = 1 r 0
- 1 ÷ 2 = 0 r 1
The value in binary is the sequence of remainders in reverse order:
10001₂ = 17
2. Log expression
The rules of logarithms tell you ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
Combining the logs into a single logarithm, we have ...
3log₂(4) -2log₂(3) +log₂(18) = log₂(4³) -log₂(3²) +log₂(18)
= log₂(4³·18/3²) = log₂(64·18/9) = log₂(128) = log₂(2⁷)
= 7
The value of the log expression is 7.
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Additional comment
A calculator can help you evaluate log expressions.
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