Question

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

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

Short answer

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

Step-by-step solution

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,$x\approx 2.302$.