Question

Evaluate: $\frac{{\left(17.42\right)}^{\frac{2}{3}}\times 18.42}{\sqrt{126.37}}$

If the answer is not an whole number then write the whole number just smaller than the answer.

[Hint: Use logarithm tables]

Answer 1

Let $y=\frac{{\left(17.42\right)}^{\frac{2}{3}}\times 18.42}{\sqrt{126.37}}$

Taking $\log$ on both sides, we get

$\ln y=\ln \left(\frac{{\left(17.42\right)}^{\frac{2}{3}}\times 18.42}{\sqrt{126.37}}\right)$

$\Rightarrow \ln y=\ln {\left(17.42\right)}^{\frac{2}{3}}+\ln 18.42-\ln \sqrt{126.37}$

$\Rightarrow \ln y=\frac{2}{3}\ln \left(17.42\right)+\ln 18.42-\frac{1}{2}\ln \left(126.37\right)$

$\Rightarrow \ln y=1.905+2.913-2.419$

$\Rightarrow \ln y=2.398$

$\Rightarrow y=$ anti $\ln 2.398$

$\Rightarrow y=11.004$

So, answer is $11$.