Help: Simple Algebra yet I fail

[Curl]

How can I go from expression 1 to expression 2? Its easy to "show" they are equivalent, but if you started with 1, how will I get to 2? I got no clue how to transform it.



1
[ (A-B)*ln(c)+( B*ln(d)-A*ln(f) ) ] /ln(d/f)

2
(A-B)*ln(c/f)/ln(d/f)+B

I bet it's cake and I'm dumb.

 

[tiny-tim]

Hi Curl!

Add B*ln(f) - B*ln(f) to the top.

 

[CompuChip]

It is possible to show this, although it is not extremely easy.
One thing you do need is that
ln(a) - ln(b) = ln(a / b).

I suggest to start by opening up the "square" brackets.
You can also add 0, in the form (A - B) ln(f) - (A - B) ln(f) = A ln(f) - B ln(f) - (A - B) ln(f).

 

[Curl]

Hi Curl!

Add B*ln(f) - B*ln(f) to the top.

haha, so I was right:

I bet it's cake and I'm dumb.

 

[CellCoree]

First of all, don't be too hard on yourself. Algebra can be a challenging subject and it's normal to struggle with certain concepts. That being said, let's take a closer look at the two expressions and see how we can go from expression 1 to expression 2.

The key to transforming expression 1 into expression 2 is to simplify each term and combine like terms. Let's break it down step by step.

Step 1: Simplify the first term
We can simplify (A-B)*ln(c) by using the logarithm rule ln(x^n) = n*ln(x). This means we can rewrite the first term as (A-B)ln(c). Similarly, we can simplify B*ln(d) to just Bln(d).

Step 2: Simplify the second term
Next, we can use the same logarithm rule to simplify A*ln(f) to just Aln(f).

Step 3: Combine like terms
Now that both terms have been simplified, we can combine like terms. We have (A-B)ln(c) and Bln(d) on the top, and Aln(f) on the bottom. In order to combine these terms, we need to find a common denominator. In this case, the common denominator is ln(d/f). Therefore, we can rewrite the expression as [(A-B)ln(c) + Bln(d)]/ln(d/f).

Step 4: Simplify the fraction
Finally, we can simplify the fraction by dividing each term by ln(d/f). This gives us the final expression of (A-B)ln(c/f)/ln(d/f) + B.

As you can see, we have transformed expression 1 into expression 2 by simplifying each term and combining like terms. Practice makes perfect, so keep working on your algebra skills and don't give up. You'll get the hang of it eventually!