Solve the logarithmic equation. Express irrational solutions in exact form and a

Chesley

Chesley

Answered question

2021-11-08

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.
logax+loga(x2)=loga(x+4)

Answer & Explanation

SoosteethicU

SoosteethicU

Skilled2021-11-09Added 102 answers

Step 1
We have to solve the logarithmic equation:
logax+loga(x2)=loga(x+4)
We know the properties of logarithms,
loga(b)+loga(c)=loga(bc)
loga(b)=loga(c)bc
Applying above properties,
loga(x)+loga(x2)=loga(x+4)
loga(x)(x2)=loga(x+4)
x(x2)=x+4
x22xx4=0
x23x4=0
Step 2
Now solving above equation by middle term splitting method,
x23x4=0
x24x+x4=0
x(x4)+1(x4)=0
(x4)(x+1)=0
Either,
x+1=0
x=-1
or,
x-4=0
x=4
Hence, solutions of the equation are x=−1, 4.

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