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

Tyra

Tyra

Answered question

2021-10-26

Solve each logarithmic equation.Express irrational solutions in exact form and as a decimal rounded to three decimal places.
log6(x+4)+log6(x+3)=1

Answer & Explanation

falhiblesw

falhiblesw

Skilled2021-10-27Added 97 answers

Step1
The properties of logarithms can be used to simplify this problem. It is observed that the logarithms are added. According to the properties of logarithms if the base of the logarithms are equal, then loga(x)+loga(y)=loga(xy) Since logarithmic functions are inverse functions of exponential functions, therefore it can be said that to eliminate the logarithmic function, it is converted into an exponential function with a base equal to the base of the logarithmic function.
Step 2
Now, using the properties of logarithms, the value of the function log6(x+4)+log6(x+3)=1 can be found. The exponential function used to eliminate the logarithmic function is 61. The resulting quadratic equation is then simplified and solved to find the different values of x
log6(x+4)+log6(x+3)=1
log6[(x+4)(x+3)]=1
x2+4x+3x+12=61
x2+7x+126=0
x2+7x+6=0
x2+6x+x+6=0
x(x+6)+1(x+6)=0
(x+1)(x+6)=0
x+1=0
x=-1
x+6=0
x=-6

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