Condene the logarithms on the left side by applying the property, ln(<em>a</em>) - ln(<em>b</em>) = ln(<em>a</em> / <em>b</em>):
ln(<em>x</em> - 2) - ln(<em>x</em> - 3) = 1
→ ln((<em>x</em> - 2) / (<em>x</em> - 3)) = 1
Now take the exponential of both sides:
exp(ln((<em>x</em> - 2) / (<em>x</em> - 3))) = exp(1)
(<em>x</em> - 2) / (<em>x</em> - 3) = <em>e</em>
Solve for <em>x</em> :
<em>x</em> - 2 = <em>e</em> (<em>x</em> - 3)
<em>x</em> - 2 = <em>e x</em> - 3<em>e</em>
<em>x</em> - <em>e x</em> = 2 - 3<em>e</em>
(1 - <em>e</em>) <em>x</em> = 2 - 3<em>e</em>
<em>x</em> = (2 - 3<em>e</em>) / (1 - <em>e</em>) ≈ 3.582
1 third is in 2/9 because when simplified 2/9 becomes 1/3 being 1 third in 2/9
Let c and d be the number of cds and dvds respectively.
c+d=12
c=12-d
The we are told that:
2c+3d=31, using c found above in this equation gives you:
2(12-d)+3d=31
24-2d+3d=31
24+d=31
d=7
So Phillip bought 7 dvds.
check...
3*7+2(12-7)=31
21+2(5)=31
21+10=31
31=31
Answer: THE LAST OPTION
Step-by-step explanation:
1. You have the following equation given in the problem:
2. If you multiply both sides of the equation shown above by 6, you obtain the following:
3. When you simplify the equation, you obtain the following equivalent equation:
here is your ans have a nice day
