Question

Use a calculator to evaluate the expression. (Do not round until the final answer. Then round to three decimal places as needed.)

Answer 1

2.303

1) For the following expression:

`(\ln30+\ln15)/(\log_(10)30+\log_(10)15)`

We can simplify that and then round it off to the nearest thousandth:

2) Let's rewrite them simplifying using the logarithm property of multiplication:

`\begin{gathered} (\ln30+\ln15)/(\log_(10)30+\log_(10)15)= \\ (\ln(30\cdot15))/(\log_(10)30+\log_(10)15)= \\ (\ln(30\cdot15))/(\log_(10)(30\cdot15))= \\ (\ln(450))/(\log_(10)(450))= \end{gathered}`

Note that the base of the Natural Log is the Euler's number "e" so let's move on now using the calculator, finally:

`(\ln(450))/(\log_(10)(450))=(6.10924)/(2.65321)=2.30258\ldots\approx2.303`

Note that only at the last step we have rounded it off. And that's the

answer