How do you solve 2lnx+3ln2=5?
1 Answer
Dec 15, 2015
Explanation:
Property of Logarithmic expression
log A + log B = Log(AB) " " " " " (1)
n log A= log A^n " " " " (2)
Given :
2ln x + 3ln 2 = 5
Rewrite as:
Using rule (1)
lnx^2 + ln2^3 = 5
Using rule (1)
ln(x^2 * 8) = 5
Raise the expression to exponential form, with the base of
e^(ln(8x^2) = e^5
8x^2 = e^5
x^2 = (e^5)/8
x = +-sqrt((e^5)/8)
x ~= 4.30716
Because the argument of any logarithm always POSITIVE and greater than zero, due to domain restriction.