Chapter 10.6, Problem 1WE

To determine

To Find:

  ${\left(1.06\right)}^{10}$

Answer to Problem 1WE

  ${\left(1.06\right)}^{10}=1.791$

Explanation of Solution

Given:

  ${\left(1.06\right)}^{10}$

Formula Used:

The log table:

  

Calculation:

Let

  $\begin{array}{l}{\left(1.06\right)}^{10}=x\\ \Rightarrow {\log }_{10}{\left(1.06\right)}^{10}={\log }_{10}x\mathrm{........}[\text{take log each side]}\\ \Rightarrow 10\log 1.06=\log x\end{array}$

We evaluate log1.06:

1. The characteristic part is 1 and mantissa part is 06.
2. Check the row number 10 and column number 6. So, the value obtained is 0253, which is the mantissa part of the solution.
3. Since the characteristic part is 1 , which is in between ${10}^0\le 1\le {10}^1$ , so the characteristic part of the solution is 0.
4. Combine the characteristic part and the mantissa part , we get, log1.06 = 0.0253.
5. So,

  $\begin{array}{l}10\log 1.06=\log x\\ \Rightarrow \log x=10(0.0253)\\ \Rightarrow \log x=0.253\\ \Rightarrow {10}^{{\log }_{10}x}={10}^{0.253}\mathrm{...............}[\text{raise 10 to the power each side of the equation]}\\ \Rightarrow x=\mathrm{1.791.......................}[b^{{\log }_{b}x}=x]\end{array}$

So, the solution is ${\left(1.06\right)}^{10}=1.791$