Brenda M.

asked • 06/04/15

Help solve

Log2 (3x+2) -log2 2=3

Steve C.

One can also get the same answer by noting that log2(2) is 1:
log2(3x+2) - 1 = 3  --> log2(3x+2) = 4  -->  3x+2 = 24  --> 3x = 16 - 2  -->  x = 14/3
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06/04/15

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Michael J. answered • 06/04/15

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When we subtract logs, we can write as a quotient of logs.
 
log2((3x + 2) / 2) = 3
 
 
The solution to a log is the exponent of the logs base number.
 
23 = (3x + 2) / 2
 
8 = (3x + 2) / 2
 
 
Multiply both sides of the equation by 2.
 
16 = 3x + 2
 
 
Subtract 2 on both sides of equation.
 
14 = 3x
 
 
Divide both sides of equation by 3.
 
14/3 = x
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