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.
log32.5 =
ln√5 =

Explanation:

Step1: Evaluate $\log(32.5)$

Using a calculator, we find that $\log(32.5)$ (assuming base 10, as it's the common logarithm) is calculated as follows:
$\log(32.5) \approx 1.511883$
Rounding to the nearest thousandth, we get $1.512$.

Step2: Evaluate $\ln(\sqrt{5})$

First, we can rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$. Then, using the property of logarithms $\ln(a^b) = b\ln(a)$, we have:
$\ln(\sqrt{5}) = \ln(5^{\frac{1}{2}}) = \frac{1}{2}\ln(5)$
Using a calculator, $\ln(5) \approx 1.609438$, so $\frac{1}{2} \times 1.609438 \approx 0.804719$
Rounding to the nearest thousandth, we get $0.805$.

Answer:

$\log(32.5) \approx \boxed{1.512}$
$\ln(\sqrt{5}) \approx \boxed{0.805}$