Using the properties of exponents and logarithms, find the value of x in 19 + 2 ln x = 25. A. 0.05 B. 1.93 C. 3 D. 20.09

Question

asked Dec 16, 2018 218k views

2 Answers

Quarkonia · Answer 1 · 2018-12-21T16:54:23+0000

Answer: D. 20.09

Explanation:

Given equation:-
$19+2\ln\ x=25$

To solve it for x, first subtract 19 from both sides of the given equation, we get

$2\ln\ x=25-19\\\Rightarrow2\ln\ x=6$

Now, divide 2 from both the sides of the equation, we get

$\ln\ x=3$

Taking exponents on both the sides, we get

$e^(\ln\ x)=e^3$

We now that exponential function is inverse of logarithmic function.

$\Rightarrow\ x=e^3\\\Rightarrow\ x=20.8553\approx20.09$