Chapter SH, Problem 7.22EP

To determine

To find: the solution of the equation and round off the solution to near ten-thousand.

Answer to Problem 7.22EP

  $\text{x=0}\text{.6284}$ .

Explanation of Solution

Given:

  ${\text{4e}}^{\text{x}}\text{-6=11}$ .

Concept used:

According the logarithmic formula:

  $\text{loge=1}$ .

  ${\text{loge}}^{\text{a}}=\text{aloge=a}$ .

The value of the logarithm can be calculated from calculator or logarithmic table.

Calculation:

Here the given equation:

  ${\text{4e}}^{\text{x}}\text{-6=11}$ .

  ${\text{e}}^{\text{x}}\text{=}\frac{17}{4}$ .

Multiplying both side $\text{log}$ operator:

  ${\text{loge}}^{\text{x}}\text{=log}\frac{17}{4}.$

According the logarithmic formula:

  $\text{loge=1}$ and ${\text{loge}}^{\text{a}}=\text{aloge=a}$ .

So, the given equation ${\text{loge}}^{\text{x}}\text{=log}\frac{17}{4}.$ can be written as:

  $\text{xloge=0}\text{.6284}$ .

Since, $\text{loge=1}$ and $\text{log}\frac{\text{29}}{\text{2}}=1.1613$ :

  $\text{x=0}\text{.6284}$ .

Hence, $\text{x=0}\text{.6284}$ .