Richiez: Excellent work! General DoubleDx

Richiez... you have the qualities of a leader.

Richiez: Excellent work! General DoubleDx

Thanks General richiez Morning bro!

ositadima1:

Richiez... you have the qualities of a leader.

I agree with you on that General Osita! Greetings

ositadima1: Richiez... you have the qualities of a leader.

General Osita i hail thee

well done guys

plz help me solve this:
Xsquare=2raise to the power of X, find the value of x?

johnpaul1101: plz help me solve this:
Xsquare=2raise to the power of X, find the value of x?

log both sides

log 2^x = log x^2
x log 2 = 2 log x
log x/x = log 2/2

Well I dont know how to continue but for me x = 2

biolabee:


log both sides

log 2^x = log x^2
x log 2 = 2 log x
log x/x = log 2/2

Well I dont know how to continue but for me x = 2

why 2?

^I think it can only be solved graphically! But 2 is correct. If you plot a graph of x^2 and that of 2^x, they will intersect at x =2 and x = 4. So these are the values of x for which x^2 = 2^x. Though there may be other points of intersection but it depends on the range of values of x you use.

johnpaul1101:
why 2?

Take a range for the value of x (eg from -2 to 5) and create a table of values for x^2 and 2^x, then plot these two graphs on the same plot. And they will intersect at x = 2 and x = 4 also at x = -0.7...something. And that would be the solution to your question!

doubleDx:

Take a range for the value of x (eg from -2 to 5) and create a table of values for x^2 and 2^x, then plot these two graphs on the same plot. And they will intersect at x = 2 and x = 4 also at x = -0.7...something. And that would be the solution to your question!

i think this your idea will lead somewhere...let me try it and see

johnpaul1101: plz help me solve this:
Xsquare=2raise to the power of X, find the value of x?

the most acceptable way to solve this is by graphical method but lets try some mathematical manipulation

X^2 = 2^x ....................(1)
taking log of both sides;
logX^2 = log2^x
2logX =Xlog2 .................(2)
NOTE
in cases like eqn(2) in which the base number on one side of the eqn is similar to the coefficient on the other side
since R.H.S = L.H.S
it implies base number on R.H.S = base number on L.H.S
similarly, coeficient on R.H.S = coeficcient on L.H.S

clearly, X=2

Richiez:

the most acceptable way to solve this is by graphical method but lets try some mathematical manipulation

X^2 = 2^x ....................(1)
taking log of both sides;
logX^2 = log2^x
2logX =Xlog2 .................(2)
NOTE
in cases like eqn(2) in which the base number on one side of the eqn is similar to the coefficient on the other side
since R.H.S = L.H.S
it implies base number on R.H.S = base number on L.H.S
similarly, coeficient on R.H.S = coeficcient on L.H.S

clearly, X=2

this is highly manipulative like u said....nd not mathematically acceptd..try it wt other values 2 verify...a great job anyway..

2nioshine: this is highly manipulative like u said....nd not mathematically acceptd..try it wt other values 2 verify...a great job anyway..

thanks, graphically i got 2.4, but i guess i made a mistake somewhere, nd i'm still working on it..,.to tell you the truth, the mathematical method is quite confusing, but thanks anyway, i'll alert you if i am able to identify and rectify the mistake...

2nioshine: this is highly manipulative like u said....nd not mathematically acceptd..try it wt other values 2 verify...a great job anyway..

that is why i said 'in cases like eqn(2) in which the base number on one side of the eqn is similar to the coefficient on the other side'
try it for any value which satisfies the statement above and you'll see i'm correct. for example try X^3 = 3^x

Ghettoguru: Help with these ones guys.

1. Integrate :

(a) ∫(x³ + 3x² + 5x +1)e^x dx
(b) ∫ln(x² + 2x) dx

2. Find the antiderivatives of the following:

(a) x sec²(x²)tan²(x²)dx
(b) x⁴dx/(4 + x²)

Question 2b

x⁴dx/(4 + x²)

To find the anti-derivative of this function, we start by using polynomial division to simplify the functiom before integrating it.

Clearly x⁴/(4 + x²) yields (x² - 4) with remainder 16 => (x² - 4) + 16/(4 + x²)
Hence ∫x⁴dx/(4 + x²) becomes =>
= ∫(x² - 4)dx + ∫16dx/(4 + x²)
= ∫(x² - 4)dx + ∫16dx/4[1 + (x²/4)]
= ∫(x² - 4)dx + ∫4dx/[1 + (x/2)²]
= x³/3 - 4x + ∫4dx/[1 + (x/2)²]

Now, from the integral formula for ∫du/[1 + (u)²] => tan^(-1)u. Applying this formula to the bolded part above yields =>
x³/3 - 4x + 8tan^(-1)(x/2) + C

:. ∫x⁴dx/(4 + x²) =>
(x³/3) - 4x + 8tan^(-1)(x/2) + C

I'll be back with the solution for question 2a.

plz dont mind my stupid question, but if i may ask....when u get to that point which states:
2logX=Xlog2
how do u determine that x=2?

johnpaul1101: plz dont mind my stupid question, but if i may ask....when u get to that point which states:
2logX=Xlog2
how do u determine that x=2?

by comparing coeficients and bases

But like i said earlier, graphical method is the most acceptable method for cases like this

@All, as far as I can tell, the only solution to that question is graphical if we are to adhere strictly to mathematical principles.Though @richiez made a good assumption. But graphically is the best and mathematically convincing solution to the question. @John try plotting the graphs with a programmable calculator if you have one!

i'll keep trying, i believe the error is from me

Do you know that u can solve the multiplication of 11 by any 2-digits by adding the 2-digits and placing the answer you get in between the 2-digits?

For example;

solve 11 * 72

7 plus 2= 9

therefore;

11 * 72= 7"9"2

11 * 72= 792

johnpaul1101: plz dont mind my stupid question, but if i may ask....when u get to that point which states:
2logX=Xlog2
how do u determine that x=2?

If you really are preparing for SSCE/UTME, you shouldn't be worried about this question because no one will ask you to solve such questions without a graph. There are more important topics you should be concentrating on and not this one. Like I said before, graphical solution is the only way if you are asked to solve any question like this one. So, be focused bruv!

Multiplication of 110 by 3-digit using the trick method:

110 * 452 =?

Solving the above multiplication' ­s not thatdifferent from that of 2-digits, the difference's just the forms of digits but both still maintain thesame rules!

Now solving;

110 * 452=

write down the first and last figures of the given 3-digits, ensure to space them,then addup the first two figures and the last two figures of the given 3-digits seperately and place the answersgotten in between the initially spaced first and last figures of the given 3-digits,then introduce zero to final answer;

4 '4 plus 5' '5 plus 2' 2 = 4972

introduce zero to the final answer:

= 4972'0'

therefore:

110 * 452 = 49720

[color=#006600][/color][url][/url][font=Lucida Sans Unicode][/font] yeaaaa....finally, X=2.....by graphical method...thanks to u all

back to simultaneous, plz help me.....i've been trying this since this evening, but i keep getting confused:
a man travels 10km in 50mins if he runs for 8km and walks for 2km. If he runs 4km and walks 6km, his time is 1hour, 15min, find his running and walking speed.

@DoubleD thank you bro, I appreciate.

johnpaul1101: back to simultaneous, plz help me.....i've been trying this since this evening, but i keep getting confused:
a man travels 10km in 50mins if he runs for 8km and walks for 2km. If he runs 4km and walks 6km, his time is 1hour, 15min, find his running and walking speed.

you know what guys lets slow down and teach him how to fish
johnpaul can u post what u have done so far
we tell u what uve done wrong
that way u learn the principles better

i really do wanna appreciate General richiez for d work he z doin on NL........u r a really good dude.....wat course are u/did u study at UNIABJ

kasbeats: i really do wanna appreciate General richiez for d work he z doin on NL........u r a really good dude.....wat course are u/did u study at UNIABJ

thanks bro, yea i'm in uniabuja CHEMICAL ENGINEERING.

biolabee: you know what guys lets slow down and teach him how to fish johnpaul can u post what u have done so far we tell u what uve done wrong that way u learn the principles better

nice idea!
@johnpaul try attempting the questn and post d solution so that we can either applaud or correct you

kasbeats: i really do wanna appreciate General richiez for d work he z doin on NL........u r a really good dude.....wat course are u/did u study at UNIABJ

we've got some other cool dudes here such as; Biolabee, Doubledx and so on wuz bn assisting me here

Richiez:
nice idea!
@johnpaul try attempting the questn and post d solution so that we can either applaud or correct you

thanks for the big up richiez