Question

exponential and logarithmic functions
using a calculator to evaluate natural and common logarithmic...
use the aleks calculator to evaluate each expression.
round your answers to the nearest thousandth.
do not round any intermediate computations.
log√7 =
log(25/3) =

Explanation:

Step1: Evaluate \( \log\sqrt{7} \)

First, simplify \( \sqrt{7} \) as \( 7^{\frac{1}{2}} \). Then, using the logarithm power rule \( \log a^b = b\log a \), we have \( \log 7^{\frac{1}{2}}=\frac{1}{2}\log 7 \). Using a calculator, \( \log 7\approx0.8451 \), so \( \frac{1}{2}\times0.8451\approx0.42255 \), rounded to the nearest thousandth is \( 0.423 \).

Step2: Evaluate \( \log\frac{25}{3} \)

Using the logarithm quotient rule \( \log\frac{a}{b}=\log a - \log b \), we get \( \log 25 - \log 3 \). Calculate \( \log 25\approx1.39794 \) and \( \log 3\approx0.47712 \). Subtracting them: \( 1.39794 - 0.47712 = 0.92082 \), rounded to the nearest thousandth is \( 0.921 \).

Answer:

\( \log\sqrt{7}\approx\boldsymbol{0.423} \), \( \log\frac{25}{3}\approx\boldsymbol{0.921} \)