Math logarithm problem!!
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Math logarithm problem!!

[From: ] [author: ] [Date: 11-09-06] [Hit: ]
x=½(-5+3√17)-...or x + 5 = 32 / x .........
Show that the equation
log2(x + 5) = 5 − log2 x
can be written as a quadratic equation in x.

Help please!
can you please give the steps too?

-
log₂(x+5)=5−log₂(x)
x>0
x+5>0
hence
x∈(0,+∞)

log₂(x+5)=5−log₂(x)
log₂(x+5)=log₂(2⁵)−log₂(x)
log₂(x+5)=log₂(32/x)
x+5=32/x
x²+5x-32=0
x₁=½(-5-3√17) <0
x₂=½(-5+3√17)


x=½(-5+3√17)

-
... log2(x + 5) = 5 − log2(x)
or log2(x + 5) = log2( 2^5 ) − log2(x)
or log2(x + 5) = log2( 32 / x )
or x + 5 = 32 / x ........ ← x > 0 ← there's not such thing as log2(0 or neg}
or x^2 + 5x = 32 ........ ← x > 0
or x^2 + 5x - 32 = 0 ... ← x > 0

-
log x+5 + log x to base 2 = 5

x[x+5] = 5 power 2 = 25

x sq + 5x- 25 = 0
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