Answer:
m = 6
Step-by-step explanation:
[tex]36^{12-m}=6^{2m}\\\\36^{12-m}=(6^{2})^{m}\\\\\36^{12-m}=36^{m}\\[/tex]
Bases are equal. so, compare the powers
12 - m = m
12 = m +m
12 = 2m
12/2 = m
6 = m
m = 6
The value of m is 6.
A power denotes the number of times a number is been multiplied by itself. For example,
6² = 6 x 6 = 36,
4³ = 4 x 4 x 4 = 64
2³ = 2 x 2 x 2 = 8
(4²)³ = [tex]4^{2\times 3}[/tex] = [tex]4^6[/tex] = [tex]4\times 4\times 4\times 4\times 4\times 4[/tex] = 4096
[tex]36^{(12-m)}=6^{2m}[/tex]
As we know 6²=36, thus we can write it as,
[tex]36^{(12-m)}=6^{2m}\\6^{2(12-m)}=6^{2m}\\[/tex]
As the bases on both the sides are equal, comparing the order(power) of both the sides,
[tex]2(12-m)=2m\\12-m = m\\12 =m+m\\2m=12\\m=\frac{12}{2}=6[/tex]
Hence, the value of m is 6.
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