Find the value of m for which 2^m x 2^2 = 23
Answers
Answer:
Step-by-step explanation:
Answer:
If the question means to say √2/3 is a root, then m = -4√2.
If the question means to say √(2/3) is a root, then m = -2√6.
Step-by-step explanation:
It is unclear in the question if √2/3 or √(2/3) is meant to be the solution. Let's do both...
Case 1
√2/3 is a solution of 3x² + mx + 2 = 0
=> 3×(√2/3)² + m×(√2/3) + 2 = 0
=> 2/3 + m×(√2/3) + 6/3 = 0
=> m×(√2/3) + 8/3 = 0
=> m×√2 + 8 = 0
=> m×√2 = -8
=> m = -8 / √2 = -8√2 / 2 = -4√2
Case 2
√(2/3) is a solution of 3x² + mx + 2 = 0
=> 3×√(2/3)² + m×√(2/3) + 2 = 0
=> 2 + m×√(2/3) + 2 = 0
=> m×√(2/3) = -4
=> m = -4√3 / √2 = -4√6 / 2 = -2√6
Answer:
m≈2.52
Step-by-step explanation:
2^m x 2^2 = 23
2^(m+2)=23
log{ 2^(m+2)=log 23
(m+2)log 2=log23
(m+2)*0.301=1.361
m+2=1.361/0.301
m+2=4.52