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Solve this equation :

[tex] \frac{3^7}{3^x}=3^2^2[/tex]

Please show all of your work, thanks! :)

Respuesta :

lilxiong
Hey there!

To start, when you have exponents with the same base, you can combine the powers. In the case of [tex] \frac{3^7}{3^x} [/tex], you can combine the two exponents by subtracting the powers from one another while keeping the base the same since you have a fraction.

This should result in this new equation:
[tex] 3^{7-x} [/tex]=[tex] 3^{22} [/tex]

Because the bases of the two numbers are the same, you can set up this expression to solve for the value of x:
7-x=22
-x=15
x=-15

Therefore, your final answer would be x=-15.

Hope this helps and have a marvelous day!
TSO
You need to know some basic rules about exponents before you can attempt to solve your question.
[tex] a^b \times a^c = a^{b+c}[/tex]
[tex] \frac{a^b}{a^c} = a^{b-c}[/tex]
[tex] (a^b)^c = a^{(b\times c)}[/tex]
[tex] a^b = a^c \Rightarrow b = c[/tex]

Knowing that, you'll see that your question is actually pretty simple.
[tex] \frac{3^7}{3^x} =3^{22} \\ \\ 3^{7-x} = 3^{22} \\ \\ 7 - x = 22\\ \\ 7 = 22 + x \\ \\ x = 7 - 22 = \boxed{\bf{-15}}[/tex]

x = -15