Q 54. - Precalculus Enhanced with Graphing Utilities

Question

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

$\frac{\log 15+\log 20}{\ln 15+\ln 20}$

Step-by-Step Solution

Answer

The value of, $\frac{\log 15+\log 20}{\ln 15+\ln 20}$is, $x\approx 0.434$.

Step 1. Given Information

The given logarithmic expression is $\frac{\log 15+\log 20}{\ln 15+\ln 20}$.

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.

$\frac{\log 15+\log 20}{\ln 15+\ln 20}$

Now, apply a scientific calculator.

Press $\left(\log \right)$ button and write the number $15$ in $( )$  after $\left(\log \right)$ .

Then press  $\left(+\right)$ button.

Press $\left(\log \right)$ button and write the number $20$ in  $( )$ after $\left(\log \right)$ .

Then press $\left(÷\right)$  button.

 

Press $\left(\ln \right)$ button and write the number $15$ in  $( )$ after $\left(\ln \right)$ .

Then press  $\left(+\right)$ button.

Press $\left(\ln \right)$ button and write the number $20$ in  $( )$ after $\left(\ln \right)$ .

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

The exact value of  $\frac{\log 15+\log 20}{\ln 15+\ln 20}$ will be

$0.4342944819$

Round the value upto three decimal places.

$0.434$

The value rounded to three decimal places  is, $x\approx 0.434$.