Solve: \ln(x)=\ln(x+6)-\ln(x-4)

necessaryh

necessaryh

Answered question

2021-10-29

Solve: ln(x)=ln(x+6)ln(x4)

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-10-30Added 109 answers

Step 1
The properties of logarithms can be used to solve the problem. Now, it is observed that the difference of the logarithms is taken. According to the properties of logarithms, ln(a)ln(b)=ln(ab) Using this property, the logarithms are simplified.
Step2
Now, when the property is used, the logarithms on the left hand side of the equation and the right hand side of the equation, have a single arguement. Hence the logarithmic terms are eliminated and the arguements are simplified to find the final value of the equation.
ln(x)=ln(x+6)ln(x4)
ln(x)=ln(x+6x4)
x(x-4)=x+6
x24x=x+6
x24xx6=0
x25x6=0
x26x+x6=0
x(x-6)+1(x-6)=0
(x-6)(x+1)=0
x=6,-1 A logarithmic function cannot have a negative argument. Hence the value of the logarithm is x=6.

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