find x if 2 raised to the power x - 7 x 5 raised to the power x minus 4 is equal to 1250
Answers
Answered by
55
Write 1250 into product of prime factors
1250= 5×5×5×5*2=5^4*2^1------(1)
Given
2^(x-7)*5^(x-4)=1250
2^x/2^7 * 5^x/5^4 =1250
Here we used
a^(m-n) = a^m/a^n
2^x * 5^x=5^4*2^1*5^4*2^7
From(1)
2^x * 5^x = 5^(4+4)*2^(1+7)
Here a^m * a^n = a ^(m+n)
(2*5)^x =(5*2)8
Here
a^m * b^m = (a*b)^m
(10)^x=(10)^8
Therefore
x=8
Since
If a^m = a^n then m=n
1250= 5×5×5×5*2=5^4*2^1------(1)
Given
2^(x-7)*5^(x-4)=1250
2^x/2^7 * 5^x/5^4 =1250
Here we used
a^(m-n) = a^m/a^n
2^x * 5^x=5^4*2^1*5^4*2^7
From(1)
2^x * 5^x = 5^(4+4)*2^(1+7)
Here a^m * a^n = a ^(m+n)
(2*5)^x =(5*2)8
Here
a^m * b^m = (a*b)^m
(10)^x=(10)^8
Therefore
x=8
Since
If a^m = a^n then m=n
Answered by
2
Step-by-step explanation:
2 - 3 x 2 - 3 power 3 whole power 3
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