if 3^x-1 - 3^x-3 = 8, then the value of (x² – X + 4) is
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Answer:10
Step-by-step explanation:x=3
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Given, 3^(x-1) - 3^(x-3) = 8
we know that (a^m)/(a^n) = a^ (m-n)
3^2*{3^(x-3)} - 3^(x-3) = 8
9 * { 3^(x-3) } - 3 ^ (x-3) = 8
8 * { 3^ (x-3) } = 8
3^ (x-3) = 8/8 = 1
We know that anything power zero is 1 i.e.
a^ 0 = 1 where, a > 0
3^ (x-3) = 1
x-3 = 0
x = 3
Then, x^2 - x + 4 = 3^2 - 3 + 4
= 9 - 3 + 4 = 8
Answer is 8
we know that (a^m)/(a^n) = a^ (m-n)
3^2*{3^(x-3)} - 3^(x-3) = 8
9 * { 3^(x-3) } - 3 ^ (x-3) = 8
8 * { 3^ (x-3) } = 8
3^ (x-3) = 8/8 = 1
We know that anything power zero is 1 i.e.
a^ 0 = 1 where, a > 0
3^ (x-3) = 1
x-3 = 0
x = 3
Then, x^2 - x + 4 = 3^2 - 3 + 4
= 9 - 3 + 4 = 8
Answer is 8
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