Can someone please show me their steps in working this out. I'm confused with the inequality flip.
In this case, you can actually solve this if you're careful. And there's no inequality flip, but I'll give an example when there is.
Here, the LHS involves an exponential, which is an increasing function. In other words, if f(a) < f(b), then a < b. Think about it. Therefore, using this property, we can write the inequality as
}} )
By the increasing property of the exponential, we can then say
} = \frac{\log{(40)}}{\log{(3)}} )
etc
However, suppose you had something like
^x < 5 )
This exponential is a decreasing function, so if f(a) > f(b), then a < b. So, doing the same as above:
^x < (\frac{1}{2})^{\log_{1/2}{(5)}} )
} )
Basically, you need to flip inequality signs if you're inverting a decreasing function, or you're dividing by a negative number.
Hi All,
I am having trouble with this question and can not work out where I am going wrong. For the most part I have it right however there is a small part that I don't. Please see the question below:
Express the following in Vertex Form.
2x^2-7x-4
My Answer: 2(x-7/4)^2-65/8
Books Answer: 2(x-7/4)^2-81/8
Any help would be greatly appreciated 
- Dylan
)
Your first task is to make the leading coefficient 1. Now deal with the bit inside the brackets.
If you ever forget how to do this, remind yourself that
^2 = x^2 + 2ax + a^2 )
^2 - a^2 )
In words, this means if you have something of the form
Check the coefficient of x. This will be 2a. Halve it to get a. Form the bracket
^2 )
and subtract
.
Applying that above, we find that
 = 2((x-\frac{7}{4})^2 - 2 - (\frac{7}{4})^2) = 2((x-\frac{7}{4})^2 - 2 - \frac{49}{16}) = 2(x-\frac{7}{4})^2 - \frac{81}{8} )
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