Hi! Can you please help me out with this question? ### Evaluate the expression without using a calculator.(a) $ \log_2 \left(\frac{1}{32}\right) = \underline{\hspace{3cm}} $(b) $ \log_9 (\sqrt{9}) = \underline{\hspace{3cm}} $(c) $ \log_{10} (0.1) = \underline{\hspace{3cm}} $(d) $ e^{\ln(\sqrt{7})} = \underline{\hspace{3cm}} $(e) $ e^{\ln\left(\frac{1}{\pi}\right)} = \underline{\hspace{3cm}} $(f) $ 10^{\log(17)} = \underline{\hspace{3cm}} $

Answered: 4. Evaluate the expression without…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Hi! Can you please help me out with this question?

### Evaluate the expression without using a calculator.

(a) $ \log_2 \left(\frac{1}{32}\right) = \underline{\hspace{3cm}} $

(b) $ \log_9 (\sqrt{9}) = \underline{\hspace{3cm}} $

(c) $ \log_{10} (0.1) = \underline{\hspace{3cm}} $

(d) $ e^{\ln(\sqrt{7})} = \underline{\hspace{3cm}} $

(e) $ e^{\ln\left(\frac{1}{\pi}\right)} = \underline{\hspace{3cm}} $

(f) $ 10^{\log(17)} = \underline{\hspace{3cm}} $

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$Apply \log rule : \log_{a} (a) = 1 a n d \log_{a} (a^{b}) = b$

$\begin{array}{rcl} \log_{2} (\frac{1}{32}) & = & \log_{2} (\frac{1}{2^{5}}) \\ = & \log_{2} (2^{- 5}) \\ = & - 5 \log_{2} (2) \\ = & - 5 \times 1 \\ = & - 5 \end{array}$