SOLUTION: Let ln (a)=2, ln (b)=3, ln (c)=5. Solve: f (x)=(ln (c^2))(ln (a^4/b^2))^-1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let ln (a)=2, ln (b)=3, ln (c)=5. Solve: f (x)=(ln (c^2))(ln (a^4/b^2))^-1      Log On


   



Question 1006514: Let ln (a)=2, ln (b)=3, ln (c)=5. Solve:
f (x)=(ln (c^2))(ln (a^4/b^2))^-1

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let ln+%28a%29=2, ln+%28b%29=3, ln+%28c%29=5.
Solve:
f+%28x%29=%28ln+%28c%5E2%29%29%28ln+%28a%5E4%2Fb%5E2%29%29%5E-1+

f+%28x%29=%28ln%285%5E2%29%29%28ln+%282%5E4%2F3%5E2%29%29%5E-1

f+%28x%29=%282%2Aln%285%29%29%284%2Aln+%282%29-2%2Aln%283%29%29%5E-1+

f+%28x%29=%282%2Aln%285%29%29%281%2F%284%2Aln+%282%29-2%2Aln%283%29%29%29+

f+%28x%29=2%2Aln%285%29%2F%284%2Aln%282%29-2%2Aln%283%29%29+

f+%28x%29=5.5945+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Let ln (a)=2, ln (b)=3, ln (c)=5. Solve:
f (x)=(ln (c^2))(ln (a^4/b^2))^-1
ln a = 2
ln b = 3
ln c = 5
f%28x%29+=+%28ln+%28c%5E2%29%29%28ln+%28a%5E4%2Fb%5E2%29%29%5E%28-+1%29
ln+%28c%5E2%29+=+2+ln+%28c%29 ------- Applying ln+%28p%5Eq%29+=+q+ln+%28p%29
%28ln+%28a%5E4%2Fb%5E2%29%29%5E%28-+1%29+=+1%2F%28ln+%28a%5E4%2Fb%5E2%29%29
We therefore have:
f%28x%29+=+2+ln+%28c%29+%2A+%281%2F%28ln+%28a%5E4%2Fb%5E2%29%29%29
f%28x%29+=+2+ln+%28c%29+%2A+%281%2F%28ln+%28a%5E4%29+-+ln+%28b%5E2%29%29%29 --- Applying ln+%28p%2Fq%29 = ln p – ln q
f%28x%29+=+2+ln+%28c%29+%2A+%281%2F%284+ln+%28a%29+-+2+ln+%28b%29%29%29 ---- Applying ln+%28p%5Eq%29 = q ln p
f%28x%29+=+2%285%29+%2A+%281%2F%284%282%29+-+2%283%29%29%29 ----------- Substituting 5 for ln c, 2 for ln a, and 3 for ln b
f%28x%29+=+10+%2A+%281%2F%288+-+6%29%29
f%28x%29+=+10+%2A+%281%2F2%29, or highlight_green%285%29