Question 1102389: If f(x)=log(2x+3), find:
a. range.
b. domain.
c. x-intercept.
d. y-intercept.
Please show your work.
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f f(x)=log(2x+3), find:
a. range.
Since 2x+3 must be > 0, range All Real Numbers
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b. domain.
Since 2x+3 must be > 0, 2x+3 > 0 ; So, domain is All Real Numbers > -3/2
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c. x-intercept.
Let y = 0 ; Then 2x+3 = 10^0 ; So x = -2/2 = -1
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d. y-intercept.
Let x = 0 ; Then y = log(3)
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Cheers,
Stan H.
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Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! f(x) = log(2x+3)
:
assume the log base is 10
:
range is all real numbers
:
domain is x > -3/2
Note negative logarithms are not defined so x can not be < -3/2
:
since log base 10 of 1 is 0, the x intercept is (-1,0)
:
y intercept is when x = 0, this gives us (0, log base 10 of 3)
:
Here is solution for x intercept (-1, 0)
:
log(10) (2x+3) = log (2x+3) / log (10)
:
log (2x+3) / log (10) = 0
:
log (2x+3) = 0
:
remove log by taking exponent of both sides of =
"
2x + 3 = 1
:
2x = -2
:
x = -1
:
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