25^2c = sqrt5 ^(4c + 16)

Question

parthkohli · Answer

Try to get the same base first.

lgbasallote · Answer

25 = 5^2
$\sqrt 5$ = 5^1/2

so just rewrite

parthkohli · Answer

$\color{Black}{\Rightarrow (5^2)^{2c} =(5^{0.5})^{4c + 16} }$

lgbasallote · Answer

$$25^{2c} = 5^{2(2c)}$$ $$\sqrt5^{(4c + 16)} = 5^{1/2(4c + 16)}$$

parthkohli · Answer

Now use the property:

$\color{Black}{\Rightarrow \large (a^x)^y = a^{xy}   }$

lgbasallote · Answer

then use the property $$a^x = a^y \implies x = y$$

anonymous · Answer

you can also eliminate the base, since they're the same. and just solve for c ^^

parthkohli · Answer

If the base is same, and we have an equals sign in between, it is obv that we'll have the same exponent.

anonymous · Answer

wow... tweeeenz!

anonymous · Answer

How do I change it to an improper fraction? I haven't done it in two years.

lgbasallote · Answer

improper fraction?

lgbasallote · Answer

where will you use that?

anonymous · Answer

My answer choices are:
a. c = 4
b. c = 7/2
c. c = -7/2
d. c = -5/2

anonymous · Answer

well it depends. what was your answer for c?

anonymous · Answer

What's that supposed to mean?

anonymous · Answer

well. okay in all cases. if you have an answer like:
2 and a quarter. you have 2 and 1/4.
so you multiply the 2 (the whole number) with the 4 (the denominator), and then add whatever's on the numerator. so the improper fraction of 2 and 1/4 is 9/4.