Question

Please help with this question thank you.

Answer 1

x = 5

Explanation:

Just as a note, you can look at x = 25 and know that it is not the answer. If it was, then you would get

4ln(25) = 2 ln(25) which reduces down to 4 = 2 when you divide by ln(25) on both sides.

4 ln(x) = 2 ln(25) Represent 25 as ln(5)^2

4 ln(x) = 2 ln(5)^2 The power on the right can be brought down.

4 ln(x) = 2 * 2 * ln(5) Divide both sides by 4

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

ln(x) = ln(5) Take the antiln of both sides.

antiln(ln(x)) = antiln(5)

x = 5

Answer 2

x = 5

Explanation:

You can rewrite the right side, then equate the arguments of the log function.

4·ln(x) = 2·ln(25)

4·ln(x) = 2·ln(5^2)

4·ln(x) = 4·ln(5) . . . . . . . use the rule ln(a^b) = b·ln(a)

x = 5 . . . . . . . . . . . . . . . .divide by 4 and take the antilog