Answer: 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 "Brainly" community!
_____________________________________________________
