Chapter 4.4, Problem 1QR

To determine

To calculate:The given value in terms of natural logarithms.

Answer to Problem 1QR

The answer in natural logarithm is $\frac{{\log }_{e}8}{{\log }_{e}5}$ .

Explanation of Solution

Given information:The value is given as,

  ${\log }_{5}8$

Formula used:The formula used to convert any base logarithm into another base logarithm is given as,

  ${\log }_{b}x=\frac{{\log }_{a}x}{{\log }_{a}b}$ ...….. (1)

Calculation:Using the equation given in equation (1),

  ${\log }_{5}8=\frac{{\log }_{e}8}{{\log }_{e}5}$

The given value is converted as $\frac{{\log }_{e}8}{{\log }_{e}5}$ .