Solve the equation. \log(x+3)=1-\log(x-2)

Phoebe

Phoebe

Answered question

2021-09-28

Solve the equation.
log(x+3)=1log(x2)

Answer & Explanation

Talisha

Talisha

Skilled2021-09-29Added 93 answers

Step 1
Given equation:
log(x+3)=1log(x2)
Solve the above equation, we get
log(x+3)+log(x2)=1
Step 2
We know that log(x)+log(y)=log(xy)
So, we have
log(x+3)+log(x2)=1
log(x+3)(x2)=1
The value pf log(10)=1
So,
log(x+3)(x2)=log(10)
(x+3)(x-2)=10
x2+x6=10
x2+x16=0
Step 3
Apply the quadratic formula
x=b±b24ac2a
Here, a=1, b=1, and c=-16
Substitute these values, we get
x=1±124×1(16)2×1
x=1±1+642
x=1±652
Step 4
Take positive sign, we get
x=1+652
Take negative sign, we get
x=1+652
We take x=1+652 because the value of x=1+652 lead to logarithm negative.
Hence the value of x=1+652

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