# Thread: Indices and Logarithms Help

1. ## Indices and Logarithms Help

hopefully can help explain these, they the last question i need to do but its mainly the reason i need
A) 2x-2 Equivalent expression 2/X-2
1/2x2 Equivalent expression ½ x -2
my problem is the reasoning for these

B) Log2(8) = 4 False My Answer - Log2(16) = 4
Log16(4)= 1/4 False My Answer - Log16(2) = 1/4
Log2(1/8)= -3 True

and again here its the reasoning but for my answers

i hope u can understand that i get it but for the reasoning i just go blank :S

2. Originally Posted by Ian360
hopefully can help explain these, they the last question i need to do but its mainly the reason i need
A) 2x-2 Equivalent expression 2/X-2
1/2x2 Equivalent expression ½ x -2
my problem is the reasoning for these

B) Log2(8) = 4 False My Answer - Log2(16) = 4
Log16(4)= 1/4 False My Answer - Log16(2) = 1/4
Log2(1/8)= -3 True

and again here its the reasoning but for my answers

i hope u can understand that i get it but for the reasoning i just go blank :S
I don't see any reason for (A).

The reasoning for (B) is this:

$\displaystyle \log_ax=n$ means $\displaystyle a^n=x$

3. Originally Posted by masters
I don't see any reason for (A).

The reasoning for (B) is this:

$\displaystyle \log_ax=n$ means $\displaystyle a^n=x$
thanks for the help on (B) cant believe how simple it is now for them

but now im stuck on the indices how can you tell if they are similar and which give products of 1..2...3 etc etc
this is what im having to do i need to match 2 with the equivant equation and also match 2 that give a product of 1...this is confusing me as in my notebook its tell me that indices are a3 + d2 something like that

4. Originally Posted by Ian360
thanks for the help on (B) cant believe how simple it is now for them

but now im stuck on the indices how can you tell if they are similar and which give products of 1..2...3 etc etc
this is what im having to do i need to match 2 with the equivant equation and also match 2 that give a product of 1...this is confusing me as in my notebook its tell me that indices are a3 + d2 something like that
I'm still not sure exactly what you're trying to do, but as far as finding products that equal 1, 2, etc.

Rewriting the rows:

$\displaystyle \frac{1}{2x^2} \ \ \ \ \frac{1}{2\sqrt{x}} \ \ \ \ \frac{2}{x} \ \ \ \ \frac{2}{\sqrt{x}} \ \ \ \ \frac{1}{2x}$

$\displaystyle 2\sqrt{x} \ \ \ \ \frac{2}{x^2} \ \ \ \ \frac{1}{2\sqrt{x}} \ \ \ \ \frac{1}{2x^2} \ \ \ \ 2x^2$
----------------------------------------------------------------------
$\displaystyle \frac{1}{2x^2}\cdot 2x^2 = 1$

$\displaystyle 2\sqrt{x} \cdot \frac{1}{2\sqrt{x}}=1$

$\displaystyle \frac{2}{x^2}\cdot 2x^2=4$

Is this what you're talking about? If so, try some products and see what happens.

5. Originally Posted by masters

I'm still not sure exactly what you're trying to do, but as far as finding products that equal 1, 2, etc.

Rewriting the rows:

$\displaystyle \frac{1}{2x^2} \ \ \ \ \frac{1}{2\sqrt{x}} \ \ \ \ \frac{2}{x} \ \ \ \ \frac{2}{\sqrt{x}} \ \ \ \ \frac{1}{2x}$

$\displaystyle 2\sqrt{x} \ \ \ \ \frac{2}{x^2} \ \ \ \ \frac{1}{2\sqrt{x}} \ \ \ \ \frac{1}{2x^2} \ \ \ \ 2x^2$
----------------------------------------------------------------------
$\displaystyle \frac{1}{2x^2}\cdot 2x^2 = 1$

$\displaystyle 2\sqrt{x} \cdot \frac{1}{2\sqrt{x}}=1$

$\displaystyle \frac{2}{x^2}\cdot 2x^2=4$

Is this what you're talking about? If so, try some products and see what happens.

thats what i was talking about thanks for the help i understand how it works now