Log3+log(4x+1)=log(x+1)+1.. Find the value of x..
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There are no solutions.
Explanation:
Use the logarithm rules to simplify either side:
Left hand side: loga+logb=log(ab)Right hand side: bloga=log(ab)
This gives
log[(x−1)(x+1)]=log[(x+2)2]
This can be simplified using the following rule:
If loga=logb, then a=b
Giving us:
(x−1)(x+1)=(x+2)2
Distribute both of these.
x2−1=x2+4x+4
Solve. The x2 terms will cancel, so there will only be one solution.
4x=−5
x=−54
However, this solution is invalid. Imagine if xactually were −54. Plug it into the original equation. The terms log(x−1) and log(x+1)would be log(−94) and log(−14), and the logarithm function loga is only defined when a>0.
Explanation:
Use the logarithm rules to simplify either side:
Left hand side: loga+logb=log(ab)Right hand side: bloga=log(ab)
This gives
log[(x−1)(x+1)]=log[(x+2)2]
This can be simplified using the following rule:
If loga=logb, then a=b
Giving us:
(x−1)(x+1)=(x+2)2
Distribute both of these.
x2−1=x2+4x+4
Solve. The x2 terms will cancel, so there will only be one solution.
4x=−5
x=−54
However, this solution is invalid. Imagine if xactually were −54. Plug it into the original equation. The terms log(x−1) and log(x+1)would be log(−94) and log(−14), and the logarithm function loga is only defined when a>0.
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Answered by
1
log(12x +3) = log (x+1) + log 10
log (12x+3) = log (10x +10)
12x + 3 = 10x +10
12x - 10x = 10 - 3
2x = 7
x = 7/2
log m + log n = logmn
log10 = 1
log (12x+3) = log (10x +10)
12x + 3 = 10x +10
12x - 10x = 10 - 3
2x = 7
x = 7/2
log m + log n = logmn
log10 = 1
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