Q 53. - Precalculus Enhanced with Graphing Utilities

Question

Use a calculator to evaluate the expression. Round your answer to three decimal places.

$\frac{\ln 4+\ln 2}{\log 4+\log 2}$

Step-by-Step Solution

Answer

The value of,  $\frac{\ln 4+\ln 2}{\log 4+\log 2}$is, $x\approx 2.302$.

Step 1. Given Information

The given logarithmic expression is $\frac{\ln 4+\ln 2}{\log 4+\log 2}$.

Step 2. Formula used

Apply a scientific calculator.

Press $\left(\ln \right)$ button and write the value of  $x$ in $( )$  after $\left(\ln \right)$ .

Press $\left(\log \right)$ button and write the value of $x$  in  $( )$ after $\left(\log \right)$ .

 

Press  $\left(=\right)$ button on the calculator.

It will give the exact value of the logarithmic number.

Round the value upto three decimal places.

Step 3. Finding Solution

Consider the given logarithm.

 $\frac{\ln 4+\ln 2}{\log 4+\log 2}$

Now, apply a scientific calculator.

Press  $\left(\ln \right)$ button and write the number $4$  in  $( )$ after $\left(\ln \right)$ .

Then press  $\left(+\right)$ button.

Press $\left(\ln \right)$ button and write the number $4$ in $( )$  after $\left(\ln \right)$ .

 

Then press $\left(÷\right)$  button.

Press $\left(\log \right)$ button and write the number $2$ in  $( )$ after $\left(\log \right)$ .

Then press $\left(+\right)$  button.

Press $\left(\log \right)$ button and write the number $2$ in  $( )$ after $\left(\log \right)$ .

 

Press $\left(=\right)$  button on the calculator.

The exact value of  $\frac{\ln 4+\ln 2}{\log 4+\log 2}$ will be

$2.302585093$

Round the value upto three decimal places.

$2.302$

The value rounded to three decimal places  is, $x\approx 2.302$.