SOLUTION: I'm not really sure how to remove the coefficients in the following problem: 2*log2(x) - log2(10) = 3*log2(4)

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Question 375439: I'm not really sure how to remove the coefficients in the following problem:
2*log2(x) - log2(10) = 3*log2(4)
Found 2 solutions by Earlsdon, ewatrrr:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
2%2ALog%5B2%5D%28x%29-Log%5B2%5D%2810%29+=+3%2ALog%5B2%5D%284%29 Use the power rule (m%2ALog%5Bb%5D%28x%29+=+Log%5Bb%5D%28x%5Em%29) to simplify.
Log%5B2%5D%28x%5E2%29-Log%5B2%5D%2810%29+=+Log%5B2%5D%284%5E3%29 Add Log%5B2%5D%2810%29 to both sides.
Log%5B2%5D%28x%5E2%29+=+Log%5B2%5D%284%5E3%29%2BLog%5B2%5D%2810%29 Simplify.
Log%5B2%5D%28x%5E2%29+=+Log%5B2%5D%2864%29%2BLog%5B2%5D%2810%29 Now apply the product rule (Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29+=+Log%5Bb%5D%28MN%29) the right side.
Log%5B2%5D%28x%5E2%29+=+Log%5B2%5D%2864%2A10%29 Simplify.
Log%5B2%5D%28x%5E2%29+=+Log%5B2%5D%28640%29 Apply the identity rule...IfLog%5Bb%5D%28M%29+=+Log%5Bb%5D%28N%29 then M+=+N
x%5E2+=+640 Take the square root of both sides.
highlight%28x+=+25.29822%29 Approx.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Note: Common properties of logarithms







2*log2(x) - log2(10) = 3*log2(4)

2*log2(x) - log2(10) - 3*log2(4)=0

log2(x^2) - log2(10) - log2(4^3)=0

log2(x^2/10*64)=0



2^0 = x^2/640

1 = x^2/640

640 = x^2

8sqrt%2810%29+=+x   Note: minus solution is extraneous