SOLUTION: Hi! I am stuck on how to find the x and y intercepts of this equation The equation goes: H(x)= logbase2(x+8) Thank you so much!!!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi! I am stuck on how to find the x and y intercepts of this equation The equation goes: H(x)= logbase2(x+8) Thank you so much!!!      Log On


   

Question 1205889: Hi! I am stuck on how to find the x and y intercepts of this equation
The equation goes:
H(x)= logbase2(x+8)
Thank you so much!!!
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

H%28x%29=+log%282%2C%28x%2B8%29%29
to find x-intercept, set H%28x%29=0
0=+log%282%2C%28x%2B8%29%29...change to base 10
0=+log%28%28x%2B8%29%29%2Flog%282%29
log%28%28x%2B8%29%29=0.....in base 10,+log%281%29=0
log%28%28x%2B8%29%29=log%281%29
x%2B8=1
x=1-8
x=-7

to find y-intercept, set x=0
H%28x%29=+log%282%2C%280%2B8%29%29
H%28x%29=+log%282%2C%288%29%29...change to base 10
H%28x%29=+log%28%288%29%29%2Flog%282%29
H%28x%29=+log%28%282%5E3%29%29%2Flog%282%29
H%28x%29=+3log%282%29%2Flog%282%29
H%28x%29=+3

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+log%282%2C%28x%2B8%29%29%29+

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.

                 (a)  x- intercept


To find x-intercept, we should solve this equation

    H(x) = 0,  or  log%282%2C%28x%2B8%29%29 = 0.


For any base logarithm, b,  if  log%28b%2C%28a%29%29 = 0,  then  a= 1.

In our case, it gives  x+8 = 1,  which implies  x= 1 - 8 = -7.    ANSWER

   

                 (b)  y- intercept


To find y-intercept, we should calculate H(0), placing x= 0:

    H(0) = log%282%2C%280%2B8%29%29 = log%282%2C%288%29%29 = 3.    ANSWER


At this point, the problem is just solved in full.

Solved.

----------------

It is not necessary to make change the logarithm base,  as the other tutor does.

In opposite,  it is simpler and it is  MORE  CORRECT  WAY  to complete the solution without changing the logarithm base.


Warning:   if in this problem you will make change of the logarithm base,
your teacher will conclude immediately that you do not know basics of logarithms.


On logarithms and their properties,  see these introductory lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator
    - Simplifying expressions with logarithms
in this site.