# Chapter 5 - Logarithmic Functions - Strengthen Your Understanding - Page 228: 31

True.

#### Work Step by Step

The number $8000$ can be compared using the inequality $$1000\leq8000\leq10000$$ Taking the $\log$ of each argument gives $$\log 1000 \leq \log 8000 \leq \log 10000$$ $$3 \leq \log 8000 \leq 4$$ Since $8000$ is closer to $10000$ than $1000$ and $\log 8000 \leq 4$, this statement is reasonable.

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