Question

30. Solve for x: 7^/10 = 2, approximate to 4 digitsa. 6.325 b. 3.256 c. 3.265 d. 3.652 e. 3.562

Answer 1

• Solution

`7^{(x)/(10)}=2`

To solve for x, we take the logarithm of both sides.

`\log 7^{(x)/(10)}=\log 2`

Applying the law of logarithm to the equation above;

`\log a^b=b\log a`
`\begin{gathered} \log 7^{(x)/(10)}=\log 2 \\ (x)/(10)\log 7=\log 2 \\ \text{Dividing both sides by log 7;} \\ (x)/(10)=(\log 2)/(\log 7) \\ (x)/(10)=(0.3010)/(0.8451) \\ (x)/(10)=0.3562 \\ \text{Cross multiplying the equation;} \\ x=0.3562*10 \\ x=3.562 \end{gathered}`

Therefore, the approximate value of x is 3.562

The correct option is E.