Respuesta :
Answer:
For given equation the value m=6
That is the value of m is 6.
Step-by-step explanation:
Given equation can be written as
[tex]36^{12-m}=6^{2m}[/tex]
Now to find the value of m in the equation:
[tex]36^{12-m}=6^{2m}[/tex]
[tex]36^{12}.36^{-m}=6^{2m}[/tex] ( using [tex]a^{m+n}=a^m.a^n[/tex]) Here m=12 and n=-m
[tex]36^{12}.36^{-m}=(6^{2})^{m}[/tex] (using [tex](a^m)^{n}=a^{mn}[/tex]) Here m=2 and n=m
[tex]\frac{36^{12}}{36^{m}}=(6^{2})^{m}[/tex] (using the property [tex]a^{m-n}=\frac{a^m}{a^n}[/tex] Here m=12 and n=m
[tex]\frac{36^{12}}{36^{m}}=36^{m}[/tex]
Now multiplying [tex]36^{m}[/tex] on both sides
[tex]\frac{36^{12}}{36^{m}}\times 36^{m}=36^{m}\times 36^{m}[/tex]
[tex]36^{12}=36^{m+m}[/tex] ( using [tex]a^{m+n}=a^m.a^n[/tex]) Here m=m and n=m
[tex]36^{12}=36^{2m}[/tex]
In the above we have base numbers are same so that we can equate the powers of these numbers
12=2m
Rewritting the equation
[tex]2m=12[/tex]
[tex]m=\frac{12}{2}[/tex]
m=6
Therefore the value of m is 6.
For given equation the value m=6.
