Is this the correct procedure for this kind of question? apparently the answer is supposed to be log6/log5.

log 3                        

= x                  

log 5

Step-by-step explanation:

25 ^x - 5^x +4 = 10

Subtract 4 from each side

25 ^x - 5^x +4-4 = 10-4

25 ^x - 5^x  = 6

25 can we rewritten as 5^2

5^2^x - 5^x  = 6

a^b^c can be written as a^(b*c)

5^(2x) - 5^x  = 6

Replace 5^x with m

m^2 - m = 6

Subtract 6 from each side

m^2 -m -6 = 6-6

m^2 -m-6=0

Factor

(m-3) (m+2) = 0

Using the zero product property

m-3 = 0   m+2=0

m=3      m=-2

Substitute m=x^2 back in

5^x =3             5^x =-2

Take the log of each side

log5 (3) =x         log5 (-2) =x

There is no  log -2  so this is not a solution

Assuming we want to use base 10

log 3                        

= x                  

log 5

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.