Given equation : [tex]25(25)^x = \frac{1}{125}[/tex]
Soltution: First we need to get rid 25 in front on left side.
25 is being multiplied by (25)^x.
We need to to apply reverse operation of multiplication, that is division.
Dividing both sides by 25, we get
[tex]\frac{25(25)^x}{25}=\frac{ \frac{1}{125}}{25}[/tex]
[tex](25)^x = \frac{1}{125*25}=\frac{1}{3125}[/tex]
Converting 25 into exponent (power) of 5 and 3125 into exponent (power) of 5.
25=5*5= (5)^2
3125= 5*5*5*5*5 or (5)^5.
Replacing 3125 by (5)^5 on right side and 25 by (5)^2 on left side.
[tex]((5)^2)^x=\frac{1}{5^5}[/tex]
Applying negative exponent rule on rigth side [tex]\frac{1}{a^n}=a^{-n}[/tex]
[tex](5)^{2x}=(5)^{-5}[/tex]
Comparing exponent on both sides, we get
2x=-5
Dividing both sides by 2, we get
2x/2 = -5/2
x=-5/2
