Solve the logarithmic equation. The logarithm equation is \ln (5-x)

CheemnCatelvew

CheemnCatelvew

Answered question

2021-09-09

Solve the logarithmic equation.
The logarithm equation is ln(5x)ln(5+x)=ln9

Answer & Explanation

Gennenzip

Gennenzip

Skilled2021-09-10Added 96 answers

Formula used:
logb(mn)=nlogbm
logb(mn)=logbmlogbn
Calculation:
The expression can be further simplified by using the exponent property of the logarithm logb(mn)=nlogbm
ln(5x)ln(5+x)=ln9
ln(5x)ln(5+x)=ln91
ln(5x)ln(5+x)=ln19
The further expression can be simplified using the division property of the logarithm. logb(mn)=logbmlogbn
ln(5x5+x)=ln19
If the equation contains only two logarithms on opposite sides of the equal sign with the same base then the problem can be solved by simply dropping the logarithm.
5x5+x=19
9(5x)=(5+x)
459x=5+x
10x=40
x=4
Conclusion:
By using the properties of logarithm, the solution of logarithmic equation is 4.

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