Answer: x = 8
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I'm going to use the notation log(2,x) to indicate "log base 2 of x". The first number is the base while the second is the expression inside the log (aka the argument of the log)
log(2,x) + log(2,(x-6)) = 4
log(2,x*(x-6)) = 4
x*(x-6) = 2^4
x*(x-6) = 16
x^2-6x = 16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x-8 = 0 or x+2 = 0
x = 8 or x = -2
Recall that the domain of log(x) is x > 0. So x = -2 is not allowed. The same applies to log(2,x) as well.
Only x = 8 is a proper solution.
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You can use the change of base rule to check your work
log base 2 of x = log(2,x) = log(x)/log(2)
log(2,(x-6)) = log(x-6)/log(2)
So,
(log(x)/log(2)) + (log(x-6)/log(2)) = 4
(log(8)/log(2)) + (log(8-6)/log(2)) = 4
(log(8)/log(2)) + (log(2)/log(2)) = 4
(log(2^3)/log(2)) + (log(2)/log(2)) = 4
(3*log(2)/log(2)) + (log(2)/log(2)) = 4
3+1 = 4
4 = 4
The answer is confirmed
Answer:
w = 12
Step-by-step explanation:
2(4w-1)=-10(w-3)+4
2*4w + 2*-1 = (10*w + 10*-3) + 4
8w - 2 = 10w - 30 + 4
8w - 2 = 10w - 26
26 - 2 = 10w - 8w
24 = 2w
w = 24/2
w = 12
Check:
2((4*12)-1) = 10(12-3) + 4
2(48-1) = 10(9) + 4
2*47 = 90 + 4 = 94
Answer:
89/35 = 2 and 19/35
Step-by-step explanation:
Answer:
cost of pizza I 5 and using proper cleaning
