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logs - c2

hi can someone tell me please the formula if you need to make the same log bases such as logbase3(2-3x)=logbase9(6x2-19x+2)

how would i make the same bases 3 what is formula thanks :wink:

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Reply 1

raheem94

Original post by otrivine

hi can someone tell me please the formula if you need to make the same log bases such as logbase3(2-3x)=logbase9(6x2-19x+2)

how would i make the same bases 3 what is formula thanks :wink:

\displaystyle log_ab = \frac{log_cb}{log_ca}

Example 1:

\displaystyle log_39

If we want to make it to the base 5.

\displaystyle log_39 = \frac{log_59}{log_53}

Example 2:

\displaystyle log_37

We want to convert it to the base 7.

\displaystyle log_37 = \frac{log_77}{log_73} =\frac1{log_73}

Reply 2

otrivine

Original post by raheem94

\displaystyle log_ab = \frac{log_cb}{log_ca}

Example 1:

\displaystyle log_39

If we want to make it to the base 5.

\displaystyle log_39 = \frac{log_59}{log_53}

Example 2:

\displaystyle log_37

We want to convert it to the base 7.

\displaystyle log_37 = \frac{log_77}{log_73} =\frac1{log_73}

one question p=logbaseq16 how can you make the base q subject?

Reply 3

TenOfThem

log_a(b) = c

b = a^c

a = b^{\frac{1}{c}} = \sqrt[c]{b}

Reply 4

otrivine

Original post by TenOfThem

log_a(b) = c

b = a^c

a = b^{\frac{1}{c}} = \sqrt[c]{b}

do we need to know that for c2 cause i am solving this one where it says
p=logbaseq16 find in terms of P
a)logbaseq2

Reply 5

raheem94

Original post by otrivine

do we need to know that for c2 cause i am solving this one where it says
p=logbaseq16 find in terms of P
a)logbaseq2

p=log_q16

Remember,

16 = 2^4

Example:

p=log_m4

You are asked to find

log_m2

in terms of

p

.

So here is how we will do it,

log_m2 = log_m\sqrt4 = log_m4^{\frac12}= \frac12 log_m4

.
We know

log_m4

equals

p

so we can write

\frac12 log_m4

\frac12 p

Reply 6

raheem94

Original post by otrivine

one question p=logbaseq16 how can you make the base q subject?

p=log_q 16

To make it the subject, use the rule,

log_a(b) = c

can be written as

a^c =b

Compare,

p=log_q 16

with

log_a(b) = c

.
Here,

p= c \ \ q=a \ \ 16 = b

So now write it in the way

a^c=b

, sub in the above data, we will get,

q^p = 16

Now to remove the power of

p

from

q

, follow the following step:

q^p = 16 \\ q^{p \times \frac1p} = 16^{\frac1p} \\ q = 16^{\frac1p}[br][br]

(edited 11 years ago)

Reply 7

TenOfThem

Original post by otrivine

do we need to know that for c2

It is the core definition of logs

Original post by otrivine

cause i am solving this one where it says
p=logbaseq16 find in terms of P
a)logbaseq2

A Raheem said this does not require anything beyond knowing that 2^4 = 16

Reply 8

otrivine

Original post by TenOfThem

It is the core definition of logs

A Raheem said this does not require anything beyond knowing that 2^4 = 16

thanks and last question ten of them this question
http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/June%202011%20-%20QP/6664_01_que_20110526.pdf

8)a) to do that how ? i got 2xpower3 for volume then what i do?

Reply 9

raheem94

Original post by otrivine

Let 'm' be the other side of the cuboid.

Remember,

\text{Volume} \ = 2x \times x \times m

We know volume equals 81, find an equation for 'm'.

L = 4(2x) + 4x +4m

Reply 10

otrivine

Original post by raheem94

Let 'm' be the other side of the cuboid.

Remember,

\text{Volume} \ = 2x \times x \times m

We know volume equals 81, find an equation for 'm'.

L = 4(2x) + 4x +4m

yep got the answer thanks and why did u put m and not x
ANd for C2 what volume and lengths and area do we need to know to be able to apply like these questions?

Reply 11

raheem94

Original post by otrivine

yep got the answer thanks and why did u put m and not x
ANd for C2 what volume and lengths and area do we need to know to be able to apply like these questions?

How do you know the other length will be 'x'?

Another length is specified as 'x' so i should now choose a different variable.

Just learn the formulas given in the book, to be honest, this part a of the question was o-level stuff.

Reply 12

otrivine

Original post by raheem94

thanks you are the best
but i did not get the question on logs where we said let p=logbaseq16 find in terms of p logbaseq2?

Reply 13

raheem94

Original post by otrivine

thanks you are the best
but i did not get the question on logs where we said let p=logbaseq16 find in terms of p logbaseq2?

I don't have any idea of explaining you without doing a solution, so i will have to go for it.

p=log_q 16 = log_q2^4 = 4log_q2 \implies \dfrac{p}4 = log_q2

\boxed{ log_q2 = \dfrac{p}{4} }

You look to be posting a lot, so i think you should consider learning LaTex.

(edited 11 years ago)

Reply 14

otrivine

Original post by raheem94

I don't have any idea of explaining you without doing a solution, so i will have to go for it.

p=log_q 16 = log_qi2^4 = 4log_q2 \implies \dfrac{p}4 = log_q2

\boxed{ log_q2 = \dfrac{p}{4} }

You look to be posting a lot, so i think you should consider learning LaTex.

thanks ok http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/June%202009/6664_01_que_20090605.pdf
question 9)a) i did h=300/2r
and sub into the the area but is not working?

Reply 15

raheem94

Original post by otrivine

thanks ok http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/June%202009/6664_01_que_20090605.pdf
question 9)a) i did h=300/2r
and sub into the the area but is not working?

You need to work hard on your basics mate.

A = \frac12 r^2 \theta = \frac12 r^2

V = A \times h

We know V= 300, find 'h' in terms of r^2.

Then find the surface area, i am assuming you are clear with the meaning of surface area.

Reply 16

otrivine

Original post by raheem94

You need to work hard on your basics mate.

A = \frac12 r^2 \theta = \frac12 r^2

V = A \times h

We know V= 300, find 'h' in terms of r^2.

Then find the surface area, i am assuming you are clear with the meaning of surface area.

how can i improve my basics for C2 please tell me raheem

what does A and H stand for in volume

(edited 11 years ago)

Reply 17

raheem94

Original post by otrivine

how can i improve my basics for C2 please tell me raheem

what does A and H stand for in volume

There is no magic wand to improve yourself.

I just used to read all the examples and solve all the questions from the book.

A stands for area.

The 'H' is 'h', and it is labelled in the diagram.

Reply 18

otrivine

Original post by raheem94

There is no magic wand to improve yourself.

I just used to read all the examples and solve all the questions from the book.

A stands for area.

The 'H' is 'h', and it is labelled in the diagram.