SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws       Log On


   

Question 197093This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Laws of Logarithms
log base 2 (log base 4 of x)= 1 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%5B2%5D%28Log%5B4%5D%28x%29%29+=+1Recalling the definition of the logarithm of a number or expression (Log%5B4%5D%28x%29):
"The logarithm of a number (Log%5B4%5D%28x%29) is the power to which the base (2) must be raised to equal that number"
Log%5B2%5D%28Log%5B4%5D%28x%29%29+=+1 can thus be written:
2%5E1+=+Log%5B4%5D%28x%29 or
Log%5B4%5D%28x%29+=+2 Applying the definition again...
4%5E2+=+x so that...
highlight%28x+=+16%29
Check:
Log%5B2%5D%28Log%5B4%5D%28x%29%29+=+1 Substitute x+=+4%5E2
Log%5B2%5D%28Log%5B4%5D%284%5E2%29%29+=+1 Apply the power rule:
Log%5B2%5D%282%2ALog%5B4%5D%284%29%29+=+1 But Log%5Bn%5D%28n%29+=+1, so
Log%5B2%5D%282%29+=+1 Again, Log%5Bn%5D%28n%29+=+1 so...
1+=+1