Express y in terms of x if,
(a) log4 y = log2 x + log2 9 - log2 3
(b) log9 y + log3 y = 2 log3 x + 3 log3 2
i need the workings please, will choose as best answer within 10 minutes
(a) log4 y = log2 x + log2 9 - log2 3
(b) log9 y + log3 y = 2 log3 x + 3 log3 2
i need the workings please, will choose as best answer within 10 minutes
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log₄(y) = log₂(x) + log₂(9) - log₂(3)
log₂(y) / log₂(4) = log₂(9x/3)
log₂(y) / 2 = log₂(3x)
log₂(y) = 2 log₂(3x)
log₂(y) = log₂((3x)²)
y = 9x²
Check:
http://www.wolframalpha.com/input/?i=sol…
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log₉(y) + log₃(y) = 2 log₃(x) + 3 log₃(2)
log₃(y)/log₃(9) + log₃(y) = log₃(x²) + log₃(2³)
log₃(y)/2 + log₃(y) = log₃(8x²)
3/2 log₃(y) = log₃(8x²)
log₃(y) = 2/3 log₃(8x²)
log₃(y) = log₃((8x²)^2/3)
y = 4 x^(4/3)
Check:
http://www.wolframalpha.com/input/?i=sol…
log₂(y) / log₂(4) = log₂(9x/3)
log₂(y) / 2 = log₂(3x)
log₂(y) = 2 log₂(3x)
log₂(y) = log₂((3x)²)
y = 9x²
Check:
http://www.wolframalpha.com/input/?i=sol…
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log₉(y) + log₃(y) = 2 log₃(x) + 3 log₃(2)
log₃(y)/log₃(9) + log₃(y) = log₃(x²) + log₃(2³)
log₃(y)/2 + log₃(y) = log₃(8x²)
3/2 log₃(y) = log₃(8x²)
log₃(y) = 2/3 log₃(8x²)
log₃(y) = log₃((8x²)^2/3)
y = 4 x^(4/3)
Check:
http://www.wolframalpha.com/input/?i=sol…
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(a) log4 y = log2 x + log2 (9/3) = log2 (x*3)
Hence: (1/2)log2 y = log2 (3x)
OR: log2 y^(1/2) = log2 (3x)
Cancel the logs:
y^(1/2) = 3x.
Square both sides:
y = 9x^2.
C'est magnifique!!
Hence: (1/2)log2 y = log2 (3x)
OR: log2 y^(1/2) = log2 (3x)
Cancel the logs:
y^(1/2) = 3x.
Square both sides:
y = 9x^2.
C'est magnifique!!