Explain how you would solve the following equation: \ln(x)+\ln(x−5)= \ln

Caelan

Caelan

Answered question

2021-11-07

Explain how you would solve the following equation:
ln(x)+ln(x5)=ln(21x)
Describe why you may only choose some of the possible roots of any polynomial you reduce the problem to
Step 1
By using the property of logarithms, simplify the LHS .
ln(a)+ln(b)=ln(ab)
Simplify the LHS
ln(x)+ln(x5)=ln(x(x5))
=ln(x25x)
Step 2
Since there is log term on both the sides of the equation, we can take antilog on both sides, simplify and solve the quadratic for x
ln(x25x)=ln(21x)
eln(x25x)=eln(21x)
x25x=x21
x25xx21=0
x24x21=0
x27x+3x21=0
x(x7)+3(x7)=0
(x7)(x+3)=0
x=7,x=3
Step 3
There are two solutions possible for value of x, one positive the other negative. However notice that in the given question there is a term ln(x). But since log of a number is defined only for x>0, we discard x=-3.
Hence the answer is x=7.

Answer & Explanation

SkladanH

SkladanH

Skilled2021-11-08Added 80 answers

Step 1
By using the property of logarithms, simplify the LHS

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