SOLUTION: what is the value of x when the equation is log5+logx=2?

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Question 118700: what is the value of x when the equation is log5+logx=2?
Found 2 solutions by m.hansen, Earlsdon:
Answer by m.hansen(16) About Me  (Show Source):
You can put this solution on YOUR website!
log5+logx=2?
remember: logs can be combined as such: Log(x) + Log(y) -> Log(x*y)
so: log(5) + log(x) = 2
becomes: log(5*x)=2 or log(5x)=2
logs can be changed into exponents, and "log" is base 10.
so: log(5x)=2 becomes: 5x= {10^2} (10^2 = 10 squared)
5x= {10^2}
5x=100
divide both sides by 5
x=20

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of x:
Log%5B10%5D%285%29%2BLog%5B10%5D%28x%29+=+2 Apply the "product rule" for logarithms:
Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29+=+Log%5Bb%5D%28MN%29 to get:
Log%5B10%5D%285x%29+=+2 Rewrite this in "exponential" form:Log%5Bb%5D%28x%29+=+y ---> x+=+b%5Ey to get:
10%5E2+=+5x Divide both sides by 5:
100%2F5+=+x so...
x+=+20
Check:
Log%5B10%5D%285%29%2BLog%5B10%5D%2820%29+=+0.69897%2B1.30103 = 2