Solve the equation. Make sure to check for extraneous solutions A) log8 (p^2+15)=2 B) 2^x=61
Solve the equation. Make sure to check for extraneous solutions
A) log8 (p^2+15)=2
B) 2^x=61
A) log8(p2 + 15) = 2
=> p2 + 15 = 82
=> p2 + 15 = 64
=> p2 + 15 - 64 = 0
=> p2 - 49 = 0
=> p2 - 72 = 0
=> (p + 7)(p - 7) = 0
=> p + 7 = 0 or p - 7 = 0
=> p = -7, +7 [Solutions]
Now, for p = -7,
log8{(-7)2 + 15) = log8(49 + 15)
= log8(64)
= log8(82)
= 2log8(8) = 2×1 = 2
For p = +7,
log8{(+7)2 + 15) = log8(49 + 15)
= log8(64)
= log8(82)
= 2log8(8) = 2×1 = 2
So, both p = -7, +7 are valid solutions.
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