Algebra Examples
Popular Problems
Algebra
Graph y = log of x
Step 1
Find the asymptotes.
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Set the argument of the logarithm equal to zero.
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Logarithm base of is .
The final answer is .
Convert to decimal.
Step 3
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Logarithm base of is .
The final answer is .
Convert to decimal.
Step 4
Find the point at .
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Replace the variable with in the expression.
The final answer is .
Convert to decimal.
Step 5
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 6
Algebra Examples
Popular Problems
Algebra
Find the Asymptotes y = log of x
Step 1
Set the argument of the logarithm equal to zero.
Step 2
The vertical asymptote occurs at .
Vertical Asymptote:
Step 3
#f(x)=log(g(x))#
The Existence Condition is
#g(x)>0#
because #log# is definited #AAx in (0,+oo)#
#g(x)=x+2#
#x+2>0#
#x> -2#
Then:
#F.E.# (Field of Existence): #(-2,+oo)#
#x=x_0=-2#
Could be a vertical asymptote if
#lim_(x rarr-2^+) f(x)=+-oo#
#lim_(x rarr-2^+) f(x)=lim_(x rarr-2^+) log(x+2)=#
#lim_(x rarr-2^+) log(0^+)=-oo#
#:. x=-2# vertical asymptote
We could looking for horizontal/slant asymptotes
#lim_(x rarr +oo) f(x)=lim_(x rarr +oo)log(x+2)=+oo#
#:.# no horizontal asymptotes
the slant asymptote formula is
#y=mx+q#
with
#m=lim_(x rarr +oo)f(x)/x#
#q=lim_(x rarr +oo)[f(x)-mx]#
#m=lim_(x rarr +oo)f(x)/x=lim_(x rarr +oo)log(x+2)/x=(+oo)/(+oo)#
Applying The L'Hopital's rule
#lim_(x rarr +oo)(h(x))/(i(x))=lim_(x rarr +oo)(h'(x))/(i'(x))#
#lim_(x rarr +oo)log(x+2)/x=lim_(x rarr +oo)(1/(x+2))/1=#
#m=lim_(x rarr +oo)1/(x+2)=0#
#q=lim_(x rarr
+oo)[f(x)-mx]=lim_(x rarr +oo)[log(x+2)-0x]=#
#=lim_(x rarr +oo)log(x+2)=+oo#
It is not finite, then #cancel(EE)# slant asymptote