Solve 5^x=4 what are the exact and approximate solutions? a. x= 1n4/1n5 ≈ 0.8614 b. x= 1n4/1n5 ≈ 1.25 c. x= 1n5/1n4 ≈ 0.8614 d. x= 1n5/1n4 ≈ 1.25

 The correct answer is:   [A]:  

            →     "  x  =  ln 4 / ln 5  ≈  0.8614 " .

Step-by-step explanation:

Given:  5ˣ = 4 ;  Solve for "x" .

Take the " ln" of each side of the equation:

       ln (5ˣ) = ln (4) ;

to get:

         x (ln 5) = ln 4 ;

Now, divide each side of the equation by:  " (ln 5) " ;

         to isolate "x" on one side of the equation;

       x (ln 5) / (ln 5)  = (ln 4) / (ln 5) ;

Note that on the "left-hand side" of the equation;

         (ln 5) / (ln 5) = 1  ; →  {and "cancels out" ;  and:

            x = ln 4 / ln 5 ;   →  which is the "exact value" ;

  →  so;  we can rule out:  " Choices:  " [C]:  &  [D]  ." ;  

                              and:  narrow our choices to:  " [A]  &  [B] . " ;

                  →  {since both answer choices:  " [A]  &  [B] " ;

                            →  provide the correct:  "exact value" ;  that is:  

                                          →     "  x  =  ln 4 / ln 5   "  .

  →  Now, using a calculator, we can determine the "approximate solution"; and hopefully, the "approximate solution" nearest to the that in the answer choice given that provides the corresponding value to the "exact value" — as well (i.e. Answer choice:  [A]: or [B] . ).  

                 →  Using a calculator, divide:  

                 →  " ln 4" by "ln 5" ; to get:

                →  " 0.8613531161467861 " ;

        →  which corresponds to:

        →   Choice:  [A]:  " 0.8514 . " (when rounded);  

                                and : " x = ln 4 / ln 5  ."  (exact value) .

The correct answer is:   [A]:  "  x  =  ln 4 / ln 5  ≈  0.8614 " .

Hope this helps!

  Best wishes in your academic endeavors

            — and within the community!

OPTION A

Step-by-step explanation:

step-by-step explanation:

0