How do you solve 2lnx+3ln2=5?

1 Answer
Dec 15, 2015

x ~= 4.30716

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

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.