First lets start with number six. The only way to solve this is if you determine what "a" and "b" are using the first log they have given to you. 
The first variable that I solved for was "a" and ![a=e^\frac{in(b)}{2}[tex]{[tex] 0](https://tex.z-dn.net/?f=%20a%3De%5E%5Cfrac%7Bin%28b%29%7D%7B2%7D%5Btex%5D%7B%5Btex%5D%20%200%3Cb%3C1%20%5Btex%5Dor%5Btex%5D%20b%3E1%20)
}
The same is also true for "b", but when you put both "a" and "b" together the only combination that I have found to work is 
Next you plug these numbers in for "a" and "b" on the second equation to get something that looks like this: ![log_\frac{1}{2}_*_\frac{1}{4} (\frac{\sqrt{\frac{1}{2}}}{\sqrt[3]{\frac{1}{4}}} )= -\frac{1}{18}](https://tex.z-dn.net/?f=%20log_%5Cfrac%7B1%7D%7B2%7D_%2A_%5Cfrac%7B1%7D%7B4%7D%20%28%5Cfrac%7B%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%20%20%29%3D%20-%5Cfrac%7B1%7D%7B18%7D%20%20%20%20%20)
and the picture below shows where the answer becomes a negative fraction.
https://www.symbolab.com/solver/logarithms-calculator/%20%5Clog_%7B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%5Cfrac%7B1%7D%7B4%7D%7D%5Cleft(%5Cfrac%7B%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%5Cright)
If you paste that link in your search bar it will give you a even more in depth understanding of how to get this answer
Next is #7, the easier of the two.There are two ways to solve for your answers. According to the graph of this equation there are four possible real solutions. 
. (This does not account for any complex solutions)
Notice that the bases are conjugates which is why the answers are so "nice"
The key is in the exponents
if 
then the sum on the conjugates will be 10 so
so 
Now for the other two
the solution is also true if 
so
the four real solutions are 
Answer:
-7 is the answer!! :) hope this helps
Answer:
The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.
⎷
(
1
)
2
+
(
2
)
2
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Step-by-step explanation:
One to any power is one.
√
1
+
(
2
)
2
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
2
to the power of
2
.
√
1
+
4
+
(
10
)
2
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
10
to the power of
2
.
√
1
+
4
+
100
+
(
6
)
2
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
6
to the power of
2
.
√
1
+
4
+
100
+
36
+
(
4
)
2
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
(
4
)
2
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
(
6
)
2
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
6
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
(
3
)
2
+
(
1
)
2
+
(
4
)
2
10
Raise
3
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
(
1
)
2
+
(
4
)
2
10
One to any power is one.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
(
4
)
2
10
Raise
4
to the power of
2
.
√
1
+
4
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
1
and
4
.
√
5
+
100
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
5
and
100
.
√
105
+
36
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
105
and
36
.
√
141
+
16
+
16
+
36
+
9
+
1
+
16
10
Add
141
and
16
.
√
157
+
16
+
36
+
9
+
1
+
16
10
Add
157
and
16
.
√
173
+
36
+
9
+
1
+
16
10
Add
173
and
36
.
√
209
+
9
+
1
+
16
10
Add
209
and
9
.
√
218
+
1
+
16
10
Add
218
and
1
.
√
219
+
16
10
Add
219
and
16
.
√
235
10
Cancel the common factor of
235
and
10
.
Tap for fewer steps...
Factor
5
out of
235
.
√
5
(
47
)
10
Cancel the common factors.
Tap for fewer steps...
Factor
5
out of
10
.
√
5
⋅
47
5
⋅
2
Cancel the common factor.
√
5
⋅
47
5
⋅
2
Rewrite the expression.
√
47
2
Rewrite
√
47
2
as
√
47
√
2
.
√
47
√
2
Multiply
√
47
√
2
by
√
2
√
2
.
√
47
√
2
⋅
√
2
√
2
Combine and simplify the denominator.
Tap for fewer steps...
Multiply
√
47
√
2
and
√
2
√
2
.
√
47
√
2
√
2
√
2
Raise
√
2
to the power of
1
.
√
47
√
2
√
2
1
√
2
Raise
√
2
to the power of
1
.
√
47
√
2
√
2
1
√
2
1
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
√
47
√
2
√
2
1
+
1
Add
1
and
1
.
√
47
√
2
√
2
2
Rewrite
√
2
2
as
2
.
Tap for fewer steps...
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
√
47
√
2
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
√
47
√
2
2
1
2
⋅
2
Combine
1
2
and
2
.
√
47
√
2
2
2
2
Cancel the common factor of
2
.
Tap for more steps...
√
47
√
2
2
1
Evaluate the exponent.
√
47
√
2
2
Simplify the numerator.
Tap for fewer steps...
Combine using the product rule for radicals.
√
47
⋅
2
2
Multiply
47
by
2
.
√
94
2
The result can be shown in multiple forms.
Exact Form:
√
94
2
Decimal Form:
4.84767985
…
Your answer my friend is in y=mx+b form: y=2/9x+26/9
or m= 2/9 and b=26/9.
