Entrepreneurrr:
Help me solve this please

the first question log(4)3 *log(3)4+log(2)32 converting the bases log(4)3=log(2)3/log(2)4 =log(2)3/2log(2)2 log to it's base is 1 so we have log(4)3= log(2)3/2 converting log(3)4 log(2)4/log(2)3 =2log(2)2/log(2)3 =2/log(2)3 lastly log(2)32=5log(2)2=5 computing we have (log(2)3/2)*(2/log(2)3)=1 so therefore log(4)3*log(3)4+log(2)32 =5+1=6

Entrepreneurrr:
Help me solve this please

second question log(2)16=4x-1 log(2)2⁴=4x-1 4log(2)2=4x-1 log(2)2=1 4=4x-1 x=5/4

Let the numbers be a and b= a+b =2p.....(i) a-b = p......(ii) eliminating 2a = 3p a= 3p/2

simiife:
Anyone please

can't sketch the diagram here 40/x=tan30 tan30°=1/√3 40/x=1/√3 x=40√3

simiife:
Anyone please

Let the numbers be a and b a+b =2p.....(i) a-b =p......(ii) eliminating 2a = 3p a= 3p/2

Entrepreneurrr:


For the first question I didn’t try it because I don’t know how to evaluate different bases.


The second one, i tried but i don’t think i got it right (see the workings)

Ok I will start with the second because I can see where you got stuck. You are finding logarithm of 4 wrongly. Its Log₂4 and not Log₁₀4. In that question Log of 4 is 2 and not 0.6021 (which you used).

Find below the detailed solution for the second question:

Obinoscopy:
Ok I will start with the second because I can see where you got stuck. You are finding logarithm of 4 wrongly. Its Log₂4 and not Log₁₀4. In that question Log of 4 is 2 and not 0.6021 (which you used).

Find below the detailed solution for the second question:

I got it boss, thanks

Entrepreneurrr:


I got it boss, thanks

Ok.

For the first question, you need to use one of the formulas of logarithm which has to do with inversion of bases:

pemisire017:
Please help me solve this question, in the diagram, O is the centre of the circle, SOR is 60 degree and PSO is 36 degree. Calculate angle PQR.

Thanks

SOR is an isosceles triangle.
Therefore, OSR=ORS=58
PSR=PSO+OSR=36+58=94

PQRS is a cyclic quadrilateral, then
PSR+PQR=180

Meaning PQR=180-94=86degrees

Spartancosta:

can't sketch the diagram here
40/x=tan30
tan30°=1/√3
40/x=1/√3
x=40√3

pls sir, am a 100 lvl student studying mechanical engineering, pls am having issues with set theory that has to do with words, i need you to just guide me, so i can be able to discern any question concerning set theory on my own

Ebube043:
pls sir, am a 100 lvl student studying mechanical engineering, pls am having issues with set theory that has to do with words, i need you to just guide me, so i can be able to discern any question concerning set theory on my own

Sir?I am sure you are older than I am.Though I'm still an aspirant,but i think I can help with sets.

Spartancosta:

Sir?I am sure you are older than I am.Though I'm still an aspirant,but i think I can help with sets.

If A={zER: e^x=0} and B={yER:a^y<0} determine n(AnB)

Ebube043:
If A={zER: e^x=0} and B={yER:a^y<0} determine n(AnB)

Thanks a bunch sir, as i await the solution, if possible you can list some good text books preferably PDFs that i can use to study

Ebube043:
If A={zER: e^x=0} and B={yER:a^y<0} determine n(AnB)

Both A and B as defined(even as there are some issues with the definition) are empty sets hence their intersection will also be empty which implies that n(AnB) = 0

Ebube043:
If A={zER: e^x=0} and B={yER:a^y<0} determine n(AnB)

A is the empty set {}. e^x is positive for all x.
If a >0, a^y>0, because a positive number to any
power is a positive number. Therefore B is the
empty set {}. The intersection of A ({}) and B ({}) is
empty ({}).
If a=0, a^y=0 for all y other than 0 (0^0 us
undefined). Therefore, B is empty ({}). The
intersection of A({}) and B({}) is empty ({}).
If a<0, a^y
=0 for y=0,
has a positive value for y=even integers,
a negative value for y=odd integers,
an imaginary value for y=rational with an even
denominator,
and weirder values (or none) for other y values.
So B={a^1, a^3, a^5, a^7, a^9, ..., a^-1, a^-3, ...}.
The intersection of A ({}) and B({...}) is empty ({}

Ebube043:
If A={zER: e^x=0} and B={yER:a^y<0} determine n(AnB)

I assume the z should be x. Apart from that, "a" is not really defined.

To solve the problem it is enough to see that A is an empty set since e^x > 0 for all xER. Since the intersection of any set with an empty is also an empty set, n(AnB)=0.

Spartancosta:

A is the empty set {}. e^x is positive for all x.
If a >0, a^y>0, because a positive number to any
power is a positive number. Therefore B is the
empty set {}. The intersection of A ({}) and B ({}) is
empty ({}).
If a=0, a^y=0 for all y other than 0 (0^0 us
undefined). Therefore, B is empty ({}). The
intersection of A({}) and B({}) is empty ({}).
If a<0, a^y
=0 for y=0,
has a positive value for y=even integers,
a negative value for y=odd integers,
an imaginary value for y=rational with an even
denominator,
and weirder values (or none) for other y values.
So B={a^1, a^3, a^5, a^7, a^9, ..., a^-1, a^-3, ...}.
The intersection of A ({}) and B({...}) is empty ({}

thanks boss for the detailed explanation,pls sit how do i become this proficient,thanks as i await your favourable response

Ebube043:
thanks boss for the detailed explanation,pls sit how do i become this proficient,thanks as i await your favourable response

just like my mentors do tell me
you have to develop interest in the subject
and most importantly,you need to PRACTICE RELENTLESSLY.

Given that \\(f(x)=2x-4\\)\nand\\(g(x)=x^{2}+3\\) then \\(f\\left ( g\\left ( x \\right ) \\right )\\)\nis\n



Help me please

officialfestus:
Given that \\(f(x)=2x-4\\)\nand\\(g(x)=x^{2}+3\\) then \\(f\\left ( g\\left ( x \\right ) \\right )\\)\nis\n



Help me please

It's not very clear

Najdorf:

It's not very clear

that's how it is

Najdorf:

It's not very clear

2x² + 2

officialfestus:
that's how it is

You copied the laTEX code.
This would be the output:

Given that
f(x)=2x-4
and
g(x)=x² + 3 then
f(g(x)) is

I believe you can carry on from here.

mathefaro:
You copied the laTEX code. This would be the output:
Given that f(x)=2x-4 and g(x)=x² + 3 then f(g(x)) is
I believe you can carry on from here.

lemme carry on boss put g inside f to find f(g(x)) f(x)=2x-4 g(x)=x²+3 f(g(x)) =2(x²+3)-4 f(g(x))=2x²+6-4 =2x²+2 it can be reversed to get g(f(x))

Very good morning to my seniors in the house, please how do i get to study the following topics in mathematics and if possible any recommendations for PDFs to Study
Scaler and vector product of two vectors
Differentiation & integration of vector with respect to scaler variable
Geometric representation of vectors 1-3 dimension
Components
Linear independence
Direction cosine.
Thanks in anticipation,God bless the helper(s)

Please I need solution to the number 4 question.the solution should be well detail thanks gurus on this thread

Ebube043:
Very good morning to my seniors in the house, please how do i get to study the following topics in mathematics and if possible any recommendations for PDFs to Study
Scaler and vector product of two vectors
Differentiation & integration of vector with respect to scaler variable
Geometric representation of vectors 1-3 dimension
Components
Linear independence
Direction cosine.
Thanks in anticipation,God bless the helper(s)

Use youtube and google. An question yku have,use quora and stackexchange.

Mathematicians in the house, please help me with the solution to this question 26.....

tolulopevoice:
Mathematicians in the house, please help me with the solution to this question 26.....

8=2^3....
2^√x=(2^3)x....comparing powers,√x=3x...x=9x^2...9x=1...
x=1/9

yusman14:
8=2^3....
2^√x=(2^3)x....comparing powers,√x=3x...x=9x^2...9x=1...
x=1/9

X=0 is also a solution.

yusman14:
8=2^3....
2^√x=(2^3)x....comparing powers,√x=3x...x=9x^2...9x=1...
x=1/9

thanks