Answer: 6x
Work Shown:
For each step, the logs are all base b. This is to save time and hassle of writing tricky notation of having to write the smaller subscript 'b' multiple times. The first rule to use is that log(x^y) = y*log(x) for any base of a logarithm. The second rule is that 
meaning that the log base of itself is 1
log(b^(6x)) = 6x*log(b) .... pull down exponent using the first rule above
log(b^(6x)) = 6x*1 .... use the second rule mentioned
log(b^(6x)) = 6x
We start with
and wish to write it as
First, pull 2 out from the first two terms:
Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have
and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square:
The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have
and when we multiply that out it does not give us what we started with. It gives us
So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.
We do this as follows:
which gives us the final expression we seek:
If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e = -103
We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106
A-2b=-10
add 2b on both sides
a=2b-10
add 10 to both sides
a+10=2b
divide both sides by 2
a/2+10/2=a/2+5=b
b=5+a/2
Answer:
$27.08 it would cost to get the other two shirts
Step-by-step explanation:
