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For what value of x is the following true? log(x+9)=logx+log9.

For what value of x is the following true?
 
log(x+9)=logx + log9

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Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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log(xy) = log x + log y
~~~~~~~~  

log(x + 9) = log x + log 9

log(x + 9) = log 9x

9x = x + 9 

8x = 9

x = 9/8
Carlos T. | Math Tutoring From Basic Algebra to Advanced CalculusMath Tutoring From Basic Algebra to Adva...
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log(x+9)=log(x)+log(9)
 
When solving logarithmic equations, you always want to put your logarithms together if their is an addition sign between two terms. For this, you use the properties of logarithms as such:
 
log(x+9)=log(9x)   ==>  [ from log(a)+log(b)=log(ab) ]
 
Now you exponentiate both sides of the equation and get:
 
x+9=9x
 
8x=9
 
x=9/8
 
 
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
-1
log(x+9) = log x + log 9
 
Since log(a) + log(b) = log(ab), 
 
log(x+9) = log (x*9)
 
 
 
Rewrite the x*9 as 9x:
 
log (x+9) = log (9x)
 
 
 
Raise 10 to both sides, which is the inverse of the log function, resulting in:
 
x+9 = 9x
 
Subtract x from both sides:
 
9 = 8x
 
Divide both sides by 8:
x = 9/8
 
 
Check:
 
log ((9/8) + 9) = log (9/8) + log 9
 
log (81/8) = log ((9/8)(9)) = log (81/8)