Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressio
1 answer:
Answer:
Therefore x=9
Step-by-step explanation:
Give that,
log x+ log (x-3) = log 54
log x(x-3) =log 54 [ ]
x(x-3) = 54
Now expand the above equation to get a quadratic equation
x²-3x=54
⇒x²-9x+6x-54=0
⇒x(x-9)+6(x-9)=0
⇒(x-9)(x+6)=0
⇒x-9=0 or, x+6=0
⇒x=9,-6
Now putting x= -6 in the given expression,
log(-6)+log(-6-9)=log 54.
Since log (-6) does not exist.
Therefore x=9
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Given:
Bees scored 9 less than three times as many points as the Hornets.
Wasps scored 28 more points than the Hornets.
Together the three teams scored 184 points.
To find:
The required equation for this scenario.
Step-by-step explanation:
Let x represent the number of points scored by the Hornets.
Bees scored 9 less than three times as many points as the Hornets.
Bees score = 3x-9
Wasps scored 28 more points than the Hornets.
Wasps score = x+28
Together the three teams scored 184 points.
Therefore, the required equation is .
Split up the interval [2, 5] into 
equally spaced subintervals, then consider the value of 
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be 
. This means the first rectangle's height would be taken to be 
when 
, so that the height is 
, and its base would have length 
. So the area under over the first subinterval is 
.
Continuing in this fashion, the area under over the 
th subinterval is approximated by 
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
The length of the interval is
Continuing in this fashion, the area under
and its value is given exactly by taking