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
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)
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
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
x[x+5] = 5 power 2 = 25
x sq + 5x- 25 = 0