Maths help

OP

i have done it which simplified to 17/3lnx
can anyone let me know if its wrong or right?
and part 2 of the question is loga x^2 + ln x^3 + 6 loga x=17/3lnx
but it doesnt quite make sense to me as there is no solution to it with my answer (ps logax does mean log base a)
Also i have another question which is a simoultaneous equations which is
lnx+2lny=ln3
lnx+lny=1
i have done it and i got
x=3e^2
y=0.1222
can you let me know if its correct becaseu when i plug them back in the equation i get 0,997 and i dont get 1 exactly

Reply 3

mqb2766

21

Original post by Selekt1234

i have done it which simplified to 17/3lnx
can anyone let me know if its wrong or right?
and part 2 of the question is loga x^2 + ln x^3 + 6 loga x=17/3lnx
but it doesnt quite make sense to me as there is no solution to it with my answer (ps logax does mean log base a)
Also i have another question which is a simoultaneous equations which is
lnx+2lny=ln3
lnx+lny=1
i have done it and i got
x=3e^2
y=0.1222
can you let me know if its correct becaseu when i plug them back in the equation i get 0,997 and i dont get 1 exactly

Can you upload your working in both cases pls?

(edited 3 years ago)

Reply 4

boulderingislife

20

Original post by Selekt1234

how do i simply this expression?
If you know how to do can you please explain it step by step

loga x^2 + ln x^3 + 6 loga x
for ln a = 3
ln(a.x^2)/ln10 +ln(x^3) + ln(a.x)/ln10 {assuming log is to base 1}

then you get:
(Ln a +lnx^2)/ln10 +(lna+ ln x)/ln10 + lnx^3
3/ln10 +2lnx/ln10 +3/ln10 + lnx/ln10 +3lnx
6/ln10+3lnx/ln10 +3lnx
(6+3lnx)/ln10 +3lnx
(6x^3 +(3x^3)lnx)/ln10

might be wrong. Too sleepy atm!

(edited 3 years ago)

Reply 5

Original post by Selekt1234

i have done it which simplified to 17/3lnx
can anyone let me know if its wrong or right?
and part 2 of the question is loga x^2 + ln x^3 + 6 loga x=17/3lnx
but it doesnt quite make sense to me as there is no solution to it with my answer (ps logax does mean log base a)
Also i have another question which is a simoultaneous equations which is
lnx+2lny=ln3
lnx+lny=1
i have done it and i got
x=3e^2
y=0.1222
can you let me know if its correct becaseu when i plug them back in the equation i get 0,997 and i dont get 1 exactly

That's not correct and I would advise leaving your answer for y (when you find it!) in terms of e rather than a decimal - it makes it easier to plug back into the original equations and check your answer.

Reply 6

OP

is x not 3e^2
if not what is it
and according to you y would be y=e^1-ln(3e^2)
and also regarding 17/3lnx
my working out
ln(a)=3
so converted everything into Ln using change of base formula
and got 1/3lnx^2+lnx^3+lnx^2 and then turned them into all lnx
2/3lnx+3lnx+2lnx=17/3lnx

Reply 7

mqb2766

21

17/3 ln(x) looks good to me.
Can you upload a pic of the original question?

(edited 3 years ago)

Reply 8

Original post by Selekt1234

is x not 3e^2
if not what is it
and according to you y would be y=e^1-ln(3e^2)

I don't get either of those values.

Take a step back and work from the basics.

You have lnx + 2lny = ln3 which means

lnx + ln(y^2) = ln3

using one of the log rules, or

ln(xy^2) = ln3

applying another log rule. So what can you say about

xy^2

?

Now trying following the same principle with the second equation and see what you can deduce about xy.

OP

x=e^1
y=1

Original post by Selekt1234

x=e^1
y=1

That pair of values satisfies the 2nd of the equations: lnx + lny = 1.

Does it satisfy the 1st equation: lnx + 2lny = ln3 ?

OP

y=e^ln3-1
x=e^2-ln3

Original post by Selekt1234

y=e^ln3-1
x=e^2-ln3

If you mean this:

y = e^{ln3 - 1}

and

x = e^{2 - ln3}

then I think those are technically correct, however, you haven't simplified them as much as you can!

How can you write those answers in simplified form?
(Hint: there shouldn't be any logarithms left in the final answer.)

Reply 13

OP

Also I have another question
Simplify
log3x+log9x
3 and 9=base
So I changed the base to 3
I got log3(x)/log3(9) which equals to 1/2log3(x) right then if I take the power up it will be log3(x^1/2)
So then it’s multiplication of log3(x X x^1/2) which =log3x^3\2
But when I keep the 1/2 and not put it as a power 1/2logx^2 so which would be the right answer

Reply 14

Original post by Selekt1234

Also I have another question
Simplify
log3x+log9x
3 and 9=base
So I changed the base to 3
I got log3(x)/log3(9) which equals to 1/2log3(x) right then if I take the power up it will be log3(x^1/2)
So then it’s multiplication of log3(x X x^1/2) which =log3x^3\2
But when I keep the 1/2 and not put it as a power 1/2logx^2 so which would be the right answer

You seem to have forgotten to add the other term when you converted

log_9(x)

to

log_3(x)

If

w = log_3(x)

then you end up with

w + (1/2)w = (3w/2) = log_3(x^{3/2})

Reply 15

OP

Original post by davros

You seem to have forgotten to add the other term when you converted

log_9(x)

to

log_3(x)

If

w = log_3(x)

then you end up with

w + (1/2)w = (3w/2) = log_3(x^{3/2})

initially I got what you got but however I put it on Photomath it gives me 1/2logx^2

(edited 3 years ago)

Reply 16